Everything aside.. why should someone even use a name given by an outsider when the original identity is sindh....it defeats the very purpose of self respect a person tries to extract out of a legacy. Pakistan could have very well named itself sindh and not Pakistan and achieved the grandeur you try to cash but since it was a modern state it was more about representation of all people it had a generic name not some name that make its people stay stuck in past.
Secondly the word indo hindu was initially only used for people around the sindh river and its tributaries..not for the whole subcontinent..it was much later in 12 century that the terminology 'Hindustan' was used for region .from Kabul to Delhi by the turkic empires and after that the rhe mughals called the what ever territory they captured east or south to be part of their original Hindustan. So you folks just adopted an identity that an invader whether it was turkic or English gave to the land.
There are lot of things in your post, I totally agree with.
Pakistan claiming the Sindh identity on a country level, would have certainly caused issues for India when it came to claiming the past culture. In a way both our countries, are descendants of the culture of the past which includes many things. However this couldn't happen, given Mr Jinnah's idea of creating a country for Muslims. Am sure we can all appreciate that, for a country going that way claiming a Non Muslim past would create confusion surely (At least that's what I think the people in Pakistan felt, given the Muslim identity at a state level they were trying to achieve at that point). This helped India in claiming this culture fully, so am a bit pleased as Indian tbh.
While I agree that we took up an identity only name wise again that I agree with you here, as Arab traders called this land Hind even before they invaded. So technically it's not a Invaders name that we adopted, it's the collective outsiders terminology that we adopted I feel for ease of going with a continuous civilization. If you take this line of viewing things, the question of self respect doesn't arise right?
As to why a name for this land, given by outsiders needed to be adopted? Given the recent 800yr past and the situation of the kingdoms, in this land before invaders taking over a name accepted by all is kind of hard I feel. Bharata Varsha (Land of Bharata, the King who is supposed to have ruled this land fully which no other King could) or Bharat is a name that could have been officially adopted, but I guess people felt for all practical purposes went with a Westernized name of India for ease of business or practicality. Hindustan or Bharat however are inter changingly used for this land, so more or less the world accepts that we are the direct descendants that Culture of Sindh.
Now this gives us advantages and disadvantages at same time. On one hand we are considered ancient culture wise, but young country wise. Whatever happened to this land, both positive and negative are ours to bear.
If you allow me, I think Pakistan in a way had a great chance breaking free of this past. Chart it's own course by becoming a country made for Muslims, and not worry about the past identity wise. I mean look to the future, rather than into the past and thus build a fully new narrative. However this hasn't come to pass I guess, given the continuous discussion about outsiders like Ghazni Ghori etc (Which I feel wasn't needed at all, for a modern nation state).