That's because Byzantium was the eastern wing of the Roman Empire. Justinian I (the emperor in the wikipedia article) is remembered for being behind the last almost successful attempt to take Rome back from the hands of the barbarians and reunite the Empire's two heads.

The two heads in the Byzantine flags, that is. Byzantines called themselves "Roman", and everyone else in the area called them "Rum" (i.e. "Roman") because they were Romans.

And this guy was the Last of the Romans:

https://en.wikipedia.org/wiki/Belisarius