The concept of Bharata/Bharatvarsha is not a new one. It is defined in scriptures, religious texts..
Besides Indika/Indians were called by travellers like Megastehsens or Arabic, Iranian , Chinese travellers..
You have to understand one thing.. It is more cultural than geographical. And it is reflected in the food, language, literature, dances, religious influences...
That is why the IVC which also included sites like Lothal or Ropar goes beyond the present defintion of nationhood
And what you said is the exact reason why your argument is so weak.
It's JUST A CONCEPT.
I don't see the big deal that people who lived somewhat close to each other had some similar facets, what are we meant to make of that?it doesn't mean a great deal to me, and clearly not to my ancestors!!
If a Christian was once a pagan, as many were, who makes a big deal about that, it was just the theme of the time, they were not attaching labels as you are.
and note that I said THEME, which does not constitute a body politic, your argument is just a patchwork of themes meshed into something way bigger then it should be.
just because a few people termed all if south Asia as India thousands of years ago is not binding my friend, it's just a convenient word to lazily describe a region.