I wouldn’t necessarily call it that. It opens up a whole can of worms about what you would consider a fair party to decide the name. The western name was India, yes.

But Bharat is derived from the Hindustani name for the region, which might have the unintended side effect of giving preference to one group of languages over others. There are many other people groups and languages that don’t speak those dialects, such as the Dravidian languages, or the Indigenous people. Seeing as they are all supposed to be equal under the law, why should one language have legitimacy over the others?

In a country as diverse as India you could say that the fairest thing would be to use a third party’s name.