The word Hindu was used initially to describe the people of India; it was never used to describe religion

Swami Vivekananda has explained it in “Rebuild India” that, mind  represents Brahman, Arms the Kshatriya, Abdomen the Vaishya and legs the Shudra. He further explains that in reality all the four Varnas exist in every human being. When he learns/teaches or uses his brains, he is Brahman. When he defends himself against any danger/atrocities, he is Kshatriya. When he earns for himself or family and engages in business/profession, he is Vaishya, and he is shudra when he uses his legs for movement. Thus every one of us is composed of all the four Varnas. In some, one is dominant and in others the other Varna.
Swami Vivekananda also said that it is unfortunate that most of the Indians don’t understand the depth of our culture.
Pundit Jawaharlal Nehru:~  The word Hindu can be earliest traced to a source a tantrik in 8th century, and it was used initially to describe the people, it was never used to describe religion. (The discovery of India” on page -74 and -75)
According to Pundit Jawaharlal Nehru Its connection with religion is of late occurrence. The word Hinduism is derived from the word Hindu.
The word Hinduism was first used by the English writers in the 19th century to describe the multiplicity of faiths of the people of India.
In Encyclopaedia Britannica it says:~  The word Hinduism was first used by the British writers in the year 1830 to describe the multiplicity of the faiths of the people of India excluding the converted Christians. (Volume -20, Reference -581)
Swami Vivekananda says:~ The word Hindu is a misnomer; the correct word should be a Vedantins, a person who follows the Vedas.
The word Hinduism is a misnomer.
Aryans were an ancient people who originally inhabited Central Asia and later migrated southwards to the regions stretching from Iran to northwest India. These early Aryans had a similar language, race, culture, and religion with many variations. The Aryans influenced by the Dravidic-culture and in later centuries other peoples also invaded and migrated to India bringing other influences and mixing many cultures ideology and beliefs.
Ancient peoples of India belong to Vedic religion or Santana Dharma therefore they have nothing to do with the present day Hinduism. The ancient peoples of Indus Valley or undivided India called Hindus by Muslim Invaders.
Vedic religion or Santana Dharma is not Hinduism. The word Hindu came originated from the word Sindhu which is another name for the river Indus. May be people who stayed along the Sindhu (Indus) valley came to be known as Hindus.
An exact date of the birth of Santana Dharma cannot be given.  They say that Santana Dharma is as old as planet earth. Some claim it is 5000 to 7000 years old Ancient India consisted of indigenous people.  Aryans, Dravidian, Jews, Christian and Muslims   have invaded India and all ingenious people were converted to different faith time to time.  Thus Hinduism is group of different caste, creed and faith.
The Hindus believed in polytheism, believing all of their Gods to be separate individuals, which were introduced much later by the founders of Hinduism which contains diverse beliefs caste and creed.
The term ‘Hindu’ is originally a geographical nomenclature. In the Arabic texts where the term ‘Hindu’ is initially used, refers to the inhabitants of the Indian subcontinent, the land across the Sindhu or Indus River. Al-Hind was, therefore, a geographical identity, and the Hindus were all the people who lived on this land.
Thus, the term ‘Hindu’ was used to describe those who professed a religion other than Islam and Christianity. It is also noteworthy that the use of the word ‘Hindu’ in non-Islamic sources is known probably only from the 15TH century A.D.
The term ‘Hindu’ became a term of administrative convenience when the rulers of Arab, Turkish, Afghan and Mughal origin ― all Muslims ― had to differentiate between ‘the believers’ and the rest.
It is a well-known fact that, the Vedic people not only did not identify themselves Hindus, but also did not possess the essential characteristics of the Hinduism. However, in order to legitimise the antiquity of Hinduism, Maharishi Sri, Dayananda Saraswathi (1824-1883) founder of Arya Samaj insisted on ‘going back to the Vedas’.
Aurobindo Ghose (1872-1950) believed that the Vedas are the foundation of the Sanatana Dharma.
Santana Dharma meaning that has no beginning or an end, righteousness for ever. Today going to a temple would make one a follower of Hinduism.
The Book of Manu was made Manu Dharma Shastra.   The Book of Manu was a book originated in India in and around 9th century A.D. This book of Manu was given a false spiritual  interpretation by orthodoxy. And this book was projected as ‘Manu Dharma Shastra’ by orthodoxy. It is the Manu Dharma Shastra is the foundation and cause for caste discrimination.
The orthodox cults which have taken upon the responsibility to maintain, propagate and perpetuate the authority of caste discriminating principle called Manu Dharma Shastra.
This caste discrimination led into umpteen numbers of castes and sub-castes within the Indian population. Today because of this caste discrimination   make the Hindus to hate each other, fight each other therefore there is no unity among the Hindus.
This caste discriminating tool is used by the modern day politicians to divide and destroy the social fabric of India.  The politicians and the orthodox cults preserve and promote Varnashrama Dharma for their own advantage, which is non-Vedic. Orthodox cults and the politicians glorify, preserve, enforce and perpetuate caste discrimination in India.
Vedas are not the important sacred scriptures for the Hindus. The Vedas as a body of scripture contains many contradictions, and they are fragmentary in nature. For most Hindus of today, scriptures like theBagavada Gita  Ramayana, Mahabharata and Puranas are more attractive and appealing than the Vedas. In addition, the gods and goddesses they worship differ considerably from the Vedic ones.
The collection of hymns called Vedas written in praise of certain deities by poets over several centuries does not seem to have much significance for the Hindus of today. Most Vedic gods do not find a place in Hinduism. Maharishi Dayananda Saraswathi fonder of Arya Samaj  was the first thinker and reformer to emphasise the importance of ‘going back to the Vedas’ in order to bring about social reforms in society and to purify Hinduism of its many aberrations. Hinduism is ‘Puranic based’. Vedic Gods like Indra, Varuna, Agni, Soma and the like, whom the Vedic people worshiped, hardly have any significance in Hinduism.
Reincarnation was not a Vedic belief.  Belief in reincarnation which is central to Hinduism of today is not really attested to in the Vedas, though they hint at life after death. The doctrine of transmigration as elaborated in Hinduism has no place in the Vedic hymns”. In the early Vedic literature, there is no express mention of the doctrine of transmigration.
It is in the Upanishads that it appears for the first time. The Rig Veda speaks of two paths for the souls of the deceased, namely, the path of the gods (devayana) and the path of the fathers (pitriyana). Those who go by the former enjoy immortality, and there is no return to physical life after that.
In fact, the Vedic man longed for this state of life. Whereas those who go by the latter path, unite with the fathers and then return to earth, after having enjoyed the fruits of his deeds.
Rig Veda ~ consisting of about 10,500 verses ― there is only one occasion where there is mention of a return to this world after death. What is implied here is that it cannot be taken as an important teaching of the Rig Veda. The Avatara and caste system are not Vedic in origin.  The theory of Avatara (‘descend’) of gods which is very important to modern Hinduism is non-Vedic. The term Avatara (…) is not found in the earlier Vedic texts and is absent from the older Sanskrit glossaries”.

The caste system which is so integral to Hinduism was also not practiced in the Vedic times. There is hardly any evidence of rigid caste system in the Vedas. It is argued that the purushasukta hymn of theRig Veda (X.90) which is often referred to in order to give a religious sanction to the  caste system, was a later interpolation. The Vedas, however, speak of various classes of people, which appear to have been names of professions, and they were not hereditary.

“The very concept of castes by birth, upper/lower castes, superior/inferior castes, out castes, untouchables, Dalits, etc. are clearly prohibited by Rigveda”.

Taboo on cow slaughter is not Vedic in origin.  The taboo on cow slaughter and beef eating did not exist in Vedic times. Criteria like taboo on beef-eating or belief in reincarnation might stamp the Vedic seers as non-Hindus”. The question whether the Vedic people practiced cow slaughter is debated among Hindu traditionalists. The cow was a sacred animal that the authors of the Vedas sacrificed cows and ate beef on special occasions. This argument only substantiates the view that cow was not an inviolable animal and that beef eating was not a taboo in Vedic times.
As is clear from the above, several aspects that are intrinsic to the Hinduism of today, such as, the doctrine of re-incarnation, avatars (‘descent’) of gods, the  caste system, taboo on cow slaughter and beef eating were absent in the Vedic religion. It was shown by a critical study of the Vedas that the Aryans had no developed idea of caste system, (.…)  The taboo on the use of beef was shown to be of later origin, that the cow was freely killed for ceremonial and other purposes in ancient India”.
Vedic religion or Santana Dharma is distinct from the Hinduism .The Vedic religion or Santana Dharma deserves to be treated on its own as a distinct religion with its own sacred texts, rites, rules of social life, beliefs and practices without inter-linking it with Hinduism. Perhaps it is right to maintain that the Mimamsa School which is concerned with the investigation of the Vedic texts, their correct interpretation and the meticulous performance of the Vedic rituals and ceremonies has preserved and defended a part of the heritage of the Vedic tradition. 
The Vedanta school also may have received a part of the inspiration from the Vedas. For the rest of the Hindu philosophical schools and religious sects, the influence of the Vedas is nominal. However, in as much as elements from the Vedas have influenced some aspects of Hinduism, it may be considered as one of the many factors influencing modern Hinduism.
But by no means can it be maintained that Hinduism has its direct ancestry in the Vedic religion or Santana Dharma. Therefore, Hinduism of Vedic times is an imagined community. Hinduism is of a much later origin, and a historical view of Indian religions would endorse a dichotomy between Vedic religion or Santana Dharma and contemporary Hinduism.
Hinduism does not have a long ancestry as is often presumed or propagated by the Hindu ideologues. In fact, historically, religions like Buddhism and Jainism can claim greater antiquity than the Hinduism of today. Hinduism began to take a systematic form from the time of Sage Sri, Sankara (8th century A.D). In this sense, he may be considered as the ‘founder’ of Hinduism.
 Thus Hinduism came to existence with its own code of conduct beliefs, rituals after 8th century.    Hinduism as one knows today is of recent origin. He states: “Hinduism did not really achieve its status as a coherent, though still baffling, religious complex until after the establishment of the British rule in indie.
In discussing the Vedic religion it is also to be remembered that in the course of history, many non-Aryan elements entered into the Vedic religion. The Vedic Aryans freely borrowed elements from the culture and the society around them. But we cannot say with precision, which are the non-Aryan elements in the Vedic religion. Therefore, the thesis of the direct ancestry of Hinduism of today from Vedic religion is to be considered as a myth purported by orthodoxy.
Temple worship, pilgrimages, the Gods and Goddesses are important to the Hindus. Hindu Gods are Rama, Krishna, Kali, Ganesh, Hanuman, Brahma, Vishnu, Shiva and the respective consorts of the last three, namely, Saraswathi, Lakshmi and Shakti. None of these deities figured prominently in the Vedic pantheon, and some of them are clearly non-Vedic. The major Gods of Hinduism like Vishnu and Shiva are non-Aryan in origin. Though they may have belonged to the Vedic tradition they played no major role in the Vedas. The more important religious sects among the Hindus, like Vaishnavism, Saivism and so on, did not have a Vedic origin, but had come into existence in much recent times.
Originally Shiva and the cult of the Mother Goddess belonged to the religion of the Indus Valley people. As one goes in deeper in the annals of  the Indian  religious history  Vishnu and Shiva cult is a melting of at least two cultures, if not three, namely, the Aryan culture, the pre-Aryan culture of the Ganges Valley and the Indus Valley culture. These three cultures were closely knit by the first century of Christianity and in the later period underwent further developments, and probably also a fourth tradition of the indigenous tribes that stood outside the four classes of the caste system as outcastes.
Vedic worshipper did not use temples and idols as Hindus of today do. For them, the sacrificial rituals were more important than temple or idol worship the major Hindu feasts of today are based on the epic feats of Rama and Krishna and the Puranic lore pertaining to Shiva and the Goddess.
Hindus are idol worshipers of the large number of Gods and Goddesses whereas the in Vedas the God has been described as:~
v  Sakshi (Witness)
v  Chetan (conscious)
v  Nirguna (Without form and properties).
v  Nitya (eternal)
v  Shuddha (pure)
v  Buddha (omniscient)
v   Mukta (unattached).
The nature of the Atman (soul) is:~
v  Witness
v  conscious
v  Without form and properties
v  eternal
v  pure
v  omniscient
v  unattached
Thus it refers to formless and attributeless God, which is the Atman (soul), the innermost self within the false experience. Thus it indicates clearly all the Gods with form and attributes are mere imagination based on the false self.  Thus Atman or soul, the innermost self is God.
The Vedas do not talk about idol worship. In fact, till about 2000 years ago followers of Vedism never worshipped idols. Idol worship was started by the followers of Buddhism and Jains.  There is logic to idol worship. Vedas speak of one God that is the supreme self in i.e. Atman or soul but Hinduism indulges in worshiping 60 million Gods.
That is why Swami Vivekananda:~
The masses in India cry to sixty million gods, and still die like dogs. Where are these gods?
 Knowing this, stand up and fight! Not one step back that is the idea. … Fight it out, whatever comes. Let the stars move from the sphere! Let the whole world stand against us! Death means only a change of garment. What of it? Thus fight! You gain nothing by becoming cowards. … Taking a step backward, you do not avoid any misfortune. You have cried to all the gods in the world. Has misery ceased? The masses in India cry to sixty million gods, and still die like dogs. Where are these gods? … The gods come to help you when you have succeeded. So what is the use? Die game. … This bending the knee to superstitions, this selling yourself to your own mind does not befit you, my soul. You are infinite, deathless, birthless. Because you are infinite spirit, it does not befit you to be a slave. … Arise! Awake! Stand up and fight! Die if you must. There is none to help you. You are the entire world. Who can help you? ~ Swami Vivekananda 
(Delivered In San Francisco, on May 28, 1900) -The Complete Works of Swami Vivekananda/Volume 1/Lectures And Discourses/The Gita II
As indicated in ISH Upanishads:~  By worshipping gods and goddesses you will go after death to the world of gods and goddesses. But will that help you? The time you spend there is wasted, because if you were not there you could have spent that time moving forward towards Self-knowledge, which is your goal. In the world of gods and goddesses you cannot do that, and thus you go deeper and deeper into the darkness.
It clearly indicates that:-If the human goal is to acquire Self-Knowledge then why one has to indulge in rituals and glorifying the conceptual gods, goddesses and gurus to go in to deeper darkness. Instead   spend that time moving forward towards Self-knowledge, which is one’s prime goal.
Since it is eternal and infinite, it comprises the only truth. The goal of Vedic religion, through the various yogas, is to realize that the consciousness (Atman) is actually nothing but Brahman.
The Vedic pantheon of gods is said, in the Vedas and Upanishads, to be only higher manifestations of Brahman. For this reason, “ekam sat” (all is one), and all is Brahman.
Thus, the goal is to realize Atman (consciousness).  If Atman (consciousness) is nothing but Brahman and by realizing Atman (consciousness) as Brahman (ultimate truth) is truth realization or Self-Realization , then there is no need to follow religion, study scriptures or glorifying gods or  gurus and  follow the path of doubts and confusion by losing oneself in the labyrinths of philosophy, when there is an easier path.  By mentally tracing the source of the mind from where it rises and subsides one becomes aware of the fallacy of the mind, which rises as waking or dream and subsides as deep sleep.  The mind raises form consciousness and subsides as consciousness.
Yajurveda says: – if one worships what is not God  

Translation 1.
They enter darkness, those who worship natural things (for example air, water, sun, moon, animals, fire, stone, etc.).
They sink deeper in darkness those who worship sambhuti. (Sambhuti means created things, for example table, chair, idol etc.)~ (Yajurveda 40:9)
Translation 2.
“Deep into shade of blinding gloom fall asambhuti’s worshippers. They sink to darkness deeper yet who on sambhuti are intent.(“Yajurveda Samhita by Ralph T. H. Giffith pg 538)
Translation 3.
“They are enveloped in darkness, in other words, are steeped in ignorance and sunk in the greatest depths of misery who worship the uncreated, eternal prakrti — the material cause of the world — in place of the All-pervading God, But those who worship visible things born of the prakrti, such as the earth, trees, bodies (human and the like) in place of God are enveloped in still greater darkness, in other words, they are extremely foolish, fall into an awful hell of pain and sorrow, and suffer terribly for a long time.” ~(Yajur Veda 40:9.)
So, Yajur Veda indicates that:~
They sink deeper in darkness those who worship sambhuti. (Sambhuti means created things, for example table, chair, idol etc. ~(Yajurved 40:9)
Those who worship visible things born of the prakrti, such as the earth, trees, bodies (human and the like) in place of God are enveloped in still greater darkness, in other words, they are extremely foolish, fall into an awful hell of pain and sorrow, and suffer terribly for a long time.~(Yajur Veda 40:9.)
The Hindus believed in polytheism, believing all of their Gods to be separate individuals, which were introduced much later by the founders of Hinduism which contains diverse beliefs caste and creed.
 When the religion of the Veda knows no idols then why so many gods and goddesses with different form and name are being propagated as Vedic gods. Why these conceptual gods are introduced when the Vedic concept of God is free from form and attributes.
Vedic religion was modified and reintroduced with new add-ons   by Sri, Sankara a great Advaita Master to uplift the Vedic culture and Santana Dharma ,  which were in ruins in the clutches of Buddhism. 18 puranas are introduced in the name of Veda Vyasa not by Sri, Sankara but someone else because the Puranic gods are non-Vedic Gods. Worship of Such Gods are barred Vedas.
 As one goes deeper in the annals of the history, it indicates the fact that somewhere someone has added the puranas in the name of Veda Vyasa the grand master of Vedas. It is impossible to accept and believe that Veda Vyasa authored and introduced puranas which has all conceptual gods.
In the year 1794 A.D. Sir William Jones, the European chief justice of the then Supreme Court of India at Calcutta, coined the new term Hinduism for the caste discriminating principle of Varnashrama Dharma originated on the basis of Manu Dharma Śāstra.
(Sir William Jones spent 11 years on the Supreme Court of Calcutta were highly productive ones, and he applied democratic principles to his judicial decisions. The six charges Jones made to the Calcutta Grand Jury during that period helped determine the course of Indian jurisprudence as well as preserve the rights of Indian citizens to trial by jury, as Jones considered Indians to be equal under the law with Europeans.
His most famous accomplishment in India was establishing the Asiatic Society of Bengal, in January of 1784. The founding of the Society grew out of Jones’s love for India, its people and its culture, as well as his abhorrence of oppression, nationalism and imperialism. His goal for the Society was to develop a means to foster collaborative international scientific and humanistic projects that would be unhindered by social, ethnic, religious and political barriers. Through the Society, Jones hoped to make Oriental studies much more attractive to people from the West. As a result, Jones exerted a substantial influence on the academic and literary disciplines in Western Europe. He would remain the Society’s president until he died.
In addition to establishing the Society, Jones felt compelled to learn Sanskrit so that he could better prepare himself to understand Hindu and Muslim laws. This led to an enormous personal project: the compilation of all such laws. The task was so huge that he was unable to complete it before he died. However, he did publish portions, including Institutes of Hindu Law, or the Ordinances of Menu, Mohammedan Law of Succession to Property of Intestates and Mohammedan Law of Inheritance. He also published numerous works about India, covering a variety of topics including law, art, music, literature, botany and geography.)
The term Hindu religion is totally a new name which cannot be found in any Indian literature prior to 1794 A.D. Out of the five Indian religions of Buddhism, Jainism, Saivism, Vaishnavism and Sikhism; Saivism and Vaishnavism were brought under the Varnashrama principle.
After naming the discriminating principle of casteism of Manu Dharma as Hindutva, the religions of Saivism and Vaishnavism, which were enslaved to the caste discriminating principles, were given a new name as ‘Hindu Religion’! Thus, Hindu religion is different from Sanatana Dharma or Vedic religion.
The term Hinduism came into existence in British rule. Hinduism is caste discriminating principle of Varnashrama Dharma based on of the Book of Manu.
After 1750 A.D., Europeans captured certain parts of India and started ruling those areas. The capital of the then British India was Calcutta the present day Kolkata.
The Britishers were duty bound to administer justice to the people living within their dominion. Thus, they set up courts of justice. They needed laws to administer justice through the courts.
To administer justice to the Christian citizens of India living within their dominion, there was Christian Law, based on Biblical principles.
To administer justice to the Muslim citizens of India living within their dominion, there was Islamic Law, based on Quranic principles. But to administer justice to non-Christian and non-Islamic citizens living in British dominion, there was no law book. This created problems for the Britishers.
At this time, Sir William Jones was appointed as the chief justice of the Supreme Court at Calcutta. Local pundits made Sir William Jones believe that the book of Manu was the law book for the people of India.
Sir William Jones believed pundits and translated the book of Manu from Sanskrit to English. Thus, on the basis of the laws of Manu, a law was formed for administering justice to non-Christian, and non-Muslim Indians of the British dominion and this law was called as the Hindu law.
The principles of the book of Manu which was used for drafting the Hindu Law were called as Hinduism. The basic principle of the book of Manu is caste discrimination.
The name coined by Sir William Jones to denote caste discriminating principles is Hinduism. It is not a religion. It is a way of Life. It is the way of life of the Indus people.
In this a historic false perception crept in. That is, when they called the terms Christian Law, Muslim law and Hindu Law, both Christian Law and Muslim Law were associated with Christian religion and Islamic religion. But in respect of Hindu Law, a false perception of religion was wrongly attributed to it as if it was also associated with a ‘Hindu religion’ which was not there.
This false perception developed a false notion that non-Christian and non-Muslim Indian of the British dominion were belonging to Hindu religion.
Out of the five Indian religions, since Saivism and Vaishnavism were already enslaved to Varnashrama dharma i.e. caste discrimination or Hindutva, the people of India began to use the newly originated common name of ‘Hindu religion’ to denote Saivism and Vaishnavism. The context and substance of the term Hinduism ; coined by Sir William Jones is different from the context and substance of this term ‘Hindu religion’, which was substituted erroneously and used by the people to denote Saivism and Vaishnavism.
The orthodox believe in Varnashrama Dharma or caste discrimination. People of India wrongly believe that the Hinduism is an   ancient religion because they are unaware of the fact that Hinduism is not the Santana Dharma or Vedic religion.
People of   India have to liberated from the strangle hold of casteism to realize their original religion is not Hinduism which is full of different caste and creeds but Vedic religion. The people should be educated about the historic truth of the religion of Vedas.