Yunan=Greece
Yunani=Greek
I think they used it even then.
I believe when Christianity took root, Greeks felt more into the Eastern Empire then a Roman would. Lets not forget it also encompassed: Phoenicia, Syria, and Egypt. The capital was set up by Romans, but the Greeks had a large amount of influence.
It is not uncommon to see some Christians call themselves Byzantine. In one Greek Orthodox Church I visited, some of their hyms were in 'Byantine.'