First of all, I don't know what you mean be "before Hindus came along," because it is a historically established fact that Hinduism predates Buddhism.
And there are plenty of Buddhist stupas in India, many of which date back as far as 200 BC. such as Sanchi. Many of the holiest sites in Buddhism are in India.
It is not uncommon for names of cities and other locations to change. By your logic, renaming Bombay as Mumbaii is biased against British heritage, because the British named the City Bombay even though the local Maratis called the area as Mumbai.
It is a historical fact that Allahbad was called Prayag before the Mughal era. Whether it should be renamed to Prayag is a whole other issue. The irony is Allahbad is actually a holy spot for Hindus, since it is the location where the Ganges and Yamuna converge.
Once again, i am not saying I support such renaming, I am simply stating a historical fact. Although you still do not seem to understand the fact that the history of India does not begin and end with Muslims.
So what were we then? Martians? Do you seriously think the Mughals were the first Empire in India? The Mauryans, Nandas, Shungas, and guptas all controlled more land than the Mughals and for a longer time.
By your logic Pakistan is only 70 years old.