According to the scriptural description of the brahmand the entire earth planet is called Bharatvarsh, but particularly the area of the continent that lies south of the Himalayas is called Bharatvarsh. It is also called Aryavart. The inhabitants of Aryavart are called the Aryans as referred to in the Rigved. Thus, the words Bhartiya or Aryans were both used for the inhabitants of Bharatvarsh or Aryavart, however, the words Bhartiya and Bharatvarsh were more popular.
Persians used to call ‘Hindu’ for the Sindhu river, which was a localized version of the word Sindhu. When Muslims invaded Bharatvarsh from the west (which was the land of the Sindhu river) they started calling the inhabitants of Bharatvarsh ‘the Hindus.’ Accordingly, the country of the Hindus was called Hindustan by them which means:
For speaking convenience the colloquial form of the word ‘sthan’ became ‘stan’ and in this way the word Hindustan (Hindu + stan) came into being. The Greeks used to call ‘Indu’ for ‘Hindu,’ because there is no letter ‘h’ in the Greek alphabet.
When English people came, for their convenience, they altered the names of quite a few places and also some of the rivers.