Why do some people call the Rhomanians "Byzantines?" Never got it.
Because in in the eighteenth century a German historian decided to start using it and then it got picked up by the Aichs school.
Rhomania end with the revolution of 1895 anyhow and the establishment of the "Hellenic Council Polity". Also it can be useful to distinguish between the various incarnations of the Roman Empire which were substantially different in almost every way from one another. Perhaps it would be more useful to speak of a Byzantine period. But either way it's a common and accepted way to describe a now extinct country whereas Rhomania is considerably less so. Even historians who've devoted their entire lives to the subject routinely still use Byzantine, at least in English academia.
Partly I suppose it has to do with the Hellenic Polity's decision to focus on their classical heritage as opposed to their imperial legacy - who can blame them after the Great Contest and the Red Decades?
I suppose I'm a little biased. It's past due that the Turks get some sort of national homeland rather than living at the periphery of Kurdistan, Syria and Greece.