oh sorry, I meant they never used the name, they definitely used the city!

I mean of course they called it byzantium when it was called that, but it was changed to constantinople when constantine upgraded it to the new capital, so it was never called byzantium during its big role in the empire if you get me.

My point is that calling the Eastern Romans "Byzantines" is a bit like calling people from France "Gauls". Like, yeah that is where Gaul was physically located, but the modern nation of France is a different thing.