Hinduism is name of Religion, and Hindu is one who has faith in that Religion. We all know that. The Indian Constitution acknowledges Hinduism as Religion, and the Indian Legal System too.
 
Let us remember that there is difference between Religion and Dharma. While Religion is the institutionalized and organizational side of Dharma, Dharma is the essence and Spiritual side of Religion. That makes Dharma accessible to every person on earth, whether he/she belongs to this Religion or that. That makes Dharma the birthright of every individual irrespective of Religion or religious identity.
 
We also know that the name Hinduism is not very ancient; the “ism” is English.
 
The Vedas do not mention the word Hindu, nor does the word find mention in any Ancient Scriptures or in Mahakavyas – Ramayana and Mahabharata. Does it matter?
 
This fact is considered a dilemma in Hinduism and for Hindus believing and practicing Hinduism. Some seek a way out by saying that Hinduism is Culture or Way of Life rather than Religion. This thought has value, no doubt; because unlike other institutionalized Religion, Hinduism has neither any central authority nor any central prophet.
 
So, what was the Original name of Hinduism or Hindu Religion?
 
No doubt, Hinduism, Hindu Religion and Hindu Dharma are considered synonymous. But as I said, there is difference between Religion and Dharma.  
 
Hindu Dharma is originally Vedic Dharma, or Upanishadik Dharma (or Vedantik); and the popular idea is that Hinduism is originally Sanatana Dharma.
 
Fact is, when we say like Vedic Dharma, Upanishadik Dharma, Sanatana Dharma or Hindu Dharma etc, we are actually qualifying the Word Dharma with pre-modifiers (adjective or functional adjective) like Vedic, Upanishadik, Sanatana, Hindu etc. I think we are limiting the scope of Dharma thus. The actual and main word is Dharma; why do we need to qualify that?
 
Dharma is Vedic word, therefore, its existence and import is more ancient than any other words. Religion is only a famous or notorious child of Dharma. One can change Religion, but no one can change or tamper with Dharma because one is born with and in Dharma, whether one while grown up accepts that or not.
 
We are often curious. Just as we say today Hindu Dharma, what did the Vedic people regard their Dharma? Did they regard themselves Vaidik? Did they call themselves Vedantik during the Upanishadik times?
 
No. These are all later names, coined for convenience of identification or for convenience of categorization.
 
What we find in Vedic Literature is that, to distinguish Dharma from Adharma, and to emphasize Dharma, the qualifiers added to Dharma were Satya and Dhruva.
 
So, if we prefer, we may say that Original name of Hindu Dharma is Satya Dharma or Dhruva Dharma; however, in my opinion, the Original name of Hinduism or Hindu Dharma is Dharma, just Dharma, and only Dharma.
 
Buddha and Mahavira adopted and retained the word Dharma, which shows Buddhism and Jainism were Reform Movements – under the umbrella and within the fold of Dharma.
 
Ashoka Maurya also preached Dharma – a synthesis of Vaidik, Upanishadik and Buddhist Dharma. It is wrong to say that Ashoka was a Buddhist, because the teachings in his Rock Edict are actually Sakama Dharma – which is one mode of Hinduism.
 
When a child is born, it has no name; and when it is given a name, it does not know the name. Only later, it learns to identify itself with the name. The newly acquired name is socially accepted; the child also falls in love with its own name. The new name does not and cannot deny the existence of the child and the child’s being prior to the name. The child may also change its name later in life. Nothing changes for that.
 
Similarly, a child learns to call its mother as “Ma”, “Mother”, “Amma” etc. only when it learns to speak. Before that, it babbles “Mummum” “Mammamamma” etc. That does not mean, the Mother has not been existing before being called by a socially accepted name. Some children even call their mother and father by adorable names not circulated in society. Neither the being of the father and mother is affected by that, nor is the children’s love for the parents and parents’ love for the children affected by that.
 
Similarly, even if Hindu and Hinduism are late names, that does not affect the Dharma, the Being that has been existing for thousands of years.
 
We may say, Hinduism is the new name of the Dharma, or we may identify our Dharma as Hindu Dharma or Sanatana Dharma.
 
It is freedom of choice that defines Hinduism.
 
Since the Indian Constitution and the Indian Legal System has accepted the words Hindu and Hinduism, and we also have a glorious tradition of the Bengal/Indian Renaissance behind acceptance of such naming, nothing matters if believers in Hinduism call themselves Hindu.
 
I would only say, let us remember, the Heart of Hindu and Hinduism is Dharma – just Dharma and only Dharma. The most ancient text RgVeda attests to that. Similarly, adding pre-modifiers to Dharma is also attested in RgVeda. Therefore, Hindus have the right and freedom of choice under Dharma to regard their Dharma as Hindu Dharma or Sanatana Dharma or the English-style Hinduism. That makes no difference.

Dharma is from ‘root’ dhr - we know that. And “r” is the content of Rta. So, etymologically, in my opinion, Dharma is dha + r + ma, which would mean – “holding + Truth + (for) happiness and welfare”; or, HOLDING ON TO TRUTH FOR HAPPINESS AND WELFARE. The implication is, Balance of Personal and Impersonal.
 
When we say Hindu Dharma, it is thus a responsibility, because Dharma – the word first mentioned in RgVeda – is the Mother of all Religion.