Both the reformed Roman Empire and the Holy Roman Empire. Played a vanilla Byzantine Empire -> Roman Empire game were my empire had shattered provinces within the HRE...
My thoughts:
Perfect: CrackdToothGrin's suggestion for different names depending on perspective (Catholic/Orthodox would probably be a good split). Too bad it's probably not doable. (Well, I suppose you could have an event which renames the realms at the start of game/whenever the player switches religion. Not very elegant though and it wouldn't work in MP)
Pretty good: Eastern Roman Empire. Related to what they actually called themselves, but not quite correct. In a way, it reflects the way the catholic world refused to recognize them as the true Rome, though not in the way it actually happened. Also different enough from the HRE.
Pretty good: Empire of the Greeks/ Greek Empire. What the catholic world called them. Fits very well for when you're playing a catholic and watching them across the map, not so much when you Orthodox, especially not when you're the Greek Empire. Gives the LoR event more power, which is great. Very different from the HRE.
Works: Byzantium. Unhistorical, but very recognizable. Has the same benefits as the Empire of the Greeks otherwise, but personally I'd say that the Rome Reformed event has less punch than if they were the Empire of the Greeks.
Works: Rhōmania. Very historical, but the least recognizable option. Good since as far, as I understand, it was an accepted term in the west. Problematic with the LoR event since either the Roman Empire should also be named in Greek, or the event will make it switch to English. Both options are a bit clunky.
Least good: Roman Empire. Accurate in their self-naming, less accurate in what the west called them. Looks weird along with the HRE. Undermines the LoR event.