Yunnan means Ionian (one of the original 4 Hellenic Phyla aka Achaeans, Dorians,Ionians, Aeolians) not Ellinas or Greek and you can meet this term even in India when they are refferring to Greeks. The Ancient Greeks never used the name Greek for themselves, they used Hellenes instead.
The people living in the Eastern Empire called themselves Romaeous (in Greek because that was their language) and their state Romania, Vasileia Romaeon or Ecoumeni. To be Romaeos you ought to speak Greek and to be Orthodox regardless of your Ethnicity.The word Hellen was used by the church as synonym to pagan till the time of the crusades when in literature begins to appear as the name of the empires inhabitants gradually replacing the term "Romaios" till the time of the Ottoman conquest. Both Plethon and Cardinal Bessarion use the term Hellenes and not Romaeoi when they reffering to the population of the Byzantine teritories.
Spyridon Trimithountios