I agree with Simetrical that the more formal aspects (diplomacy) of the game should use the Political name, while less formal ones like armies and stuff should use the people.

This is a really hard question to have an ironclad rule though for, as many people have pointed out, so I would say unless you do something along Simetrical's lines (rough base) I would say the people's names in general for gaming ease. If you have tons of long names in foreign languages, people won't really care too much and just use the current name. Eg if you use that long carthage name instead of Tsorim, I'll just think of them as Carthage. As of now even when playing vanilla, I'm hyped enough that I already think of carthage as Tsorim. So for aesthetic reasons I would say the people's names (from what I know)

I hope this thread ain't all out of date and this was a waste of typing.