Yes, thats true. I know several old men back to my island who never call themselves other than "Romios/Romioi". But that was the way the Byzantine (err...whatever) administration tried to make understood to the westerners that the eastern empire was the righteous bearer of the Roman Imperial inheiritance. For the same reason the Germans called their empire as Holy Roman Empire. As far as I know the Byzantine maps named the HRE as Germania, or Vasilio ton Germanon (Kingdom of the Germans) and the western maps named the ERE/Byzantium as "The empire of the Greeks (well I have only sea a French 1300+AD and a Venician of 1424AD).