If you look up in respectable history books, you will find that:
Name "Byzantine" refers to the
Eastern Roman Empire (330-1453 AD), centred in Constantinople (modern day Istanbul) known for it’s distinct
Greek-Speaking culture, magnificent art.
There were Greeks living in the Eastern Roman Empire as minority. Only place where Greeks in clear majority were in lands now occupied by current Greece. Otherwise Byzantine was the Eastern Roman Empire established by the Romans. As the most common language spoken among the population was Greek (It was a bit like when a Turk and an Arab meet they speak to each other in English. ), the Roman Emperor Heraclius in 620 AD declared the language of the Empire as Greek.
Before 620 AD the legal language of the empire was Latin. After losing Egypt then Levant, the core of the empire had become mostly Greek speakers among themselves, although not necessarily being Greek. .
As an example, There were around 400000 Kipchak Turks living in Karaman/Turkey in 1920. They had accepted Orthodox Christian belief. But did not speak Greek. They spoke Turkish. These were brought from eastern Europe by the Byzantines to fight for them. During population exchange at least 200000 of them were shipped to Greece.
The Byzantine empire consisted of many nationalities. Not counting the original inhabitants like Lydians, Sumerians, Hittites, Urartians, Assyrians, Celts and Persians who had amalgamated and somehow were lost in the soup; it included:
Armenians,
Slavs,
Arabs,
Syrians,
Georgians,
Copts,
Bulgarians,
Albanians,
Goths,
Vlachs, and
Jews. Not just Greeks.
