They actually called themselves Ῥωμαῖοι, not Romani, and not every description needs to be emic. There's nothing wrong with the label "Byzantine" except to Byzaboos.
But Wikipedia[0] says Ῥωμαῖοι transliterates to Romaioi, i.e. "Romans".
[0] https://en.wikipedia.org/wiki/Byzantine_Empire#Nomenclature
So I shouldn't call them Romans, since that is an English translation of what they called themselves, and thus foreign to them.
But you can call them Byzantines, an English term invented in the 19th century, because... you say so? Thank you, I have been enlightened.
> Byzaboos
Hey that's fresh. Do they have Hittitomori too?