What is the correct word for Hindi speaker, is it the Hindu or the Indian?
Hindi is not the language of the Hindus, it never was.
India is a potpourri of varied sects and religions.
Hindi (हिन्दी), or more precisely Modern Standard Hindi (मानक हिन्दी), is a standardised and Sanskritised register of the Hindustani language.
Hindustani (Hindustani: हिन्दुस्तानी, ہندوستانی[a]), historically also known as Hindavi, Dehlvi, Urdu, and Rekhta, is the lingua franca of North India and Pakistan. (wiki)
Currently there are 22 official languages in India. A plurality of speakers in India speak Hindi. Indian from every religion - i.e., Muslims, Jews, Christians, Budhhists, Jains etc. speak/can speak in Hindi.
An Indian court clarified that Hindi is not the national language of India because the constitution does not mention it as such. Outside of Asia, Hindi is also an official language in Fiji.
A Hindi speaker from the most populous Northern states is termed "native Hindi-speaker".
Someone who speaks Hindi can be a Muslim Irishman or a German Jew.
What language someone speaks (even as a mother tongue!) does not necessarily mean anything about that person's geographical or ethnic background.
An Indian is someone from India. They can speak many languages, and Hindi might be one. They may identify with Hinduism religiously, culturally or socially, but they may be Muslims or Christian or Buddhist or whatever.
A Hindu is someone who identifies religiously, culturally or socially with Hinduism, but they may speak many languages, and Hindi might be one. They may be German, English, American or come from or live anywhere else in the world.
A speaker of Hindi is someone who speaks the Hindi language. They may identify with Hinduism religiously, culturally or socially, but they may be Muslims or Christian or Buddhist or whatever. They may be German, English, American or come from or live anywhere else in the world.
Given that someone who speaks French can be called a Francophone, and someone who speaks English can be called an Anglophone, one could use the same standard and refer to speakers of Hindi as Hindiphones. While this may not be an already-established word in the English lexicon, many words in English were contrived. So, say "Namaste" to the Hindiphones in your life!
In the language Hindi, the correct single word for somebody who speaks Hindi would be hindibhashi (हिन्दीभाषी), the literal translation of which is "one who speaks Hindi." There is no regional or religious or other identity associated with this than the literal meaning.
There is no single word translation of that in English.
The answer by Mysti Sinha gives great background on the language and many things associated with it.
I believe the word you are looking for is - HINDIPHONE. https://en.wiktionary.org/wiki/hindiphone