Hard disagree. They were Roman. They called themselves as such. Were called Romans even by their enemies. The term Byzantine empire or calling then Greeks was done due to doctrinal and political disputes and wanting to delegitimize the eastern empire. What right does some historian or people 500 years after the empires death have to say someone wasn’t Roman when they called themselves Roman and even their enemies did too? All this stuff about them not being laying speakers or being Greek is nonsense. The eastern empire was Greek speaking since the time of Alexander and even before him. And your whole thing about them being in disputes with the west is nonsensical and invalid. That doesn’t effect their Romanness. When the empire split for the final time with the death of theodosius I the two empires had the same government and army and bureaucracy and laws and it’s people were Roman citizens and everything. The eastern empire changed in many ways but Rome had a long long history and changed in many ways during that time. They never stopped being Roman and to call them anything else is ridiculous.