[cwnyth]

Because I was too brief while at work before, let me be fuller now: if you were to go back a thousand years and ask about the national characteristic of the emperor of Constantinople, they'd look at you crazy because you spoke English. But your question is laden with several assumptions that are completely foreign to their minds. First, Byzantine is an adjective from Byzantium, the original name of Constantinople. First and foremost, when its used in Classical and Late Antique historiography, it's describing an empire, culture, polity, etc. that centers on Constantinople, rather than other cities of the empire. It is not an ethnic marker. The people at the time would have called themselves Greek, Romans, or Syrians. Second, whether "Romaioi" or "Hellenes" is preferred waxes and wanes depending on what's en vogue at the time. Contrary to the meme, the citizens of Athens did not uniformly call themselves "Romans" (Romaioi) from the 320s onward. Some were, some weren't. What language did they speak? What ethnos, genos were they of? What does Romaioi even really mean? That will yield better answers, but again, it differs based on fashion. Lastly, the very idea of a defined "empire" would be very confusing for the ancients. What is that word? It looks like imperium, but that means domain of rule. It's not limited to those at the helm, who might call themselves imperatores, but also Augusti. It's not like a kingdom encompassing other kingdoms. It's just a modern term given to an ancient reality, with no difference at all to names like Byzantine or even Roman.

See e.g. Lintott on the problems of this terminology:

https://www.cambridge.org/core/journals/greece-and-rome/arti...

This whole "debate" is a charade provided by people who once complained they had to take a humanities class and thereafter were clueless about what real modern historians and philologists were discussing about this period.