João III
King
In fairness, I never claimed I was making an original point! (but I appreciate the snarkI think everyone is aware the Eastern Roman Empire was never called the Byzantine Empire in its time. People do love to point out the same widely known facts over and over as if they are making original points.
Anyway, it was a separate entity, A) because it had already become a de-facto separate state from the Western Roman empire whilst that still existed, and B) because over time it's Greek language and later Orthodox faith came to be significant in defining its character.
We aren't really concerned with what they called themselves, after all, Mehmed II proclaimed himself Kayser-i Rûm on the conquest of Constantinople. Distinguishing them from the Western Roman Empire is done because it is most useful and makes sense.

My point was that following the logic of your other comments, China should be split up in this game for those very same reasons.
Hmm maybe I should've added a follow-up question of "would you rather see China split or Rome and Byzantium combined?"TBH I agree with this statement. Problem being this is not how OP phrase his/her question.
I don't mind having multiple China(s) in a Civ game - or, China would fit Huamnkind's "per era" model better - but "Byzantines-Romans" is an entirely different beast to deal with.
Edit: I've added this question to the OP