Is it legitimate for the Eastern Roman Empire to claim the legacy? I think so, and I think they have among the best arguments for it. Conversely it is also legitimate to note the major differences between the two and the fact that discontinuities do exist.
I'm not denying that gradually, over well more than a thousand years, the empire (only surviving in the East) changed character in many ways. I am denying that a unique Eastern character sprang up (and immediately applied to Egypt) the moment that Constantinople was founded.
I do agree with you that there was no instantaneous Eastern character that sprang up out of nowhere.
But you can call them Byzantines, an English term invented in the 19th century, because... you say so? Thank you, I have been enlightened.
You're also arguing against a strawman. I never said they weren't Roman. I only said there's nothing wrong with Byzantine.
Maybe if you weren't so smugly self-righteous, you'd have better reading comprehension.
Hey that's fresh. Do they have Hittitomori too?
[0] https://en.wikipedia.org/wiki/Byzantine_Empire#Nomenclature
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.