I do not know whether there is an Indian name meaning Queen of India: in modern times many people use many things as names: apocryphally, someone named their daughter `nIl AkAshe ekTi tArA' which means `a [lone] star in the blue sky' in Bengali. Furthermore, India speaks a variety of languages, most of which belong to two language families. The constitution guarantees the freedom to use any one of twenty languages in most official settings, the number of mutually unintelligible dialects running into 100s, and I know very few of them.
Most religions have various extreme versions, but by and large, very few sects of Hinduism would think that the `Queen' has to be a Hindu. Moreover, Hinduism does not `define' most people who think of themselves as Hindu: religion may well form the source of their cultural and moral values, it certainly does not colour their rational views about the world. A queen is a secular title and not a religious one, so there is no perceived conflict according to most Hindus.
Also, India is not Hindu alone. There is a large 15% of others, most of whom are Muslims, but there are a large number of Parsees, not to mention the Jain, Buddhist, Jewish and Christian people. Also, the fraction would have been smaller if the British census did not force Indians to classify their religion into their predefined notions: larging forging Hindu and Muslim identities as a byproduct.
Finally, it is not a linguistic question. Hindus speak all the 100s of dialects, and they do have words for Queen, and a word for India.
Calling Mother Teresa, a very respected figure incidentally, as the Queen is something I am not familiar with, and feels very non-Indian to me: queen in most contexts connotes concepts of wealth, and maybe beauty, but not spirit. Her deep human empathy would be insulted by such an epithet: she was like a mother to many and her kindness much appreciated, her belief in only one right way of being in touch with the Supreme, and her evangelism, much less so.
Queen of India is also problematic because the concept has to be modern: after the first few centuries of the common era, the concept of monarch of the entire subcontinent does not reappear till the mughal period (and, incidentally, they were muslims). And, typically the muslim queens wanted to be called things like `light of the world' rather than `queen of India'. (I mean the queens who were wives of the monarchs; Razia Sultana the queen who was a monarch in the period just before the mughals probably had no time to call herself anything and stay above court intrigue.)
In the modern era, the title `bhArata samrAjJi' (the J is a nasal sound like the n~ of Spanish; jJ is pronounced variously from gy to dn in various parts of India) meaning `Empress of India' does appear in the literature.
Sorry, could not help, but got confused by the earlier errors. Bailing out.