I'm Eastern Orthodox, so trust me, I know.
Did you know Istanbul is the same word as Constantinople? It's like a slang version.
I'm probably talking to a Greek person, so I can't really say anything smart and not offend you. Kyrie eleison Kyrie eleison kyrie eleison... ;-)
The Byzantines primary language was Greek. Followed by Latin, and included most of what is today, modern Turkey.
Turkey was not even a thought at that time. Calling it Turkish would be appropriation of the Greek culture.