What is old name of India?

The name India came from the name Indus (from the Sindhu river.)
When Europeans arrived in India they could spell Hindustan or Bharat. So, they named the land as the land of Indus. Thus, it got its name India.

In Persian, they'd always drop the S from a Sanskrit word and add an H which made it Hind(h)u

It was then changed by the Greeks from Hindu to Indos.

The latin of Indos is Indus

And finally the Romans gave us India