The roman empire consisted of theRoman (western mediterranean), and Rome’s conquest of the Greek Empire (Aegean), Greek-Conquered Egypt, and Anatolia, Roman conquered Syria, Palestine, and North Africa.
The greek (eastern empire) survived, but the west was lost to jewish internal insurrection and Germanian external conquest, and the rest incrementally lost to judaism v3, the muslim conquests, which destroyed every great civilization of the ancient world.
So the eastern empire was roman in name the same way the holy roman empire was roman (neither was).