I’ve read that the Byzantines fully thought as themselves as Romans and never referred to themselves as “Byzantines.” Why is it that we distinct the Byzantine Empire from the Roman Empire outside of the popular language being Greek instead of Latin? Weren’t the Eastern Provinces of the Roman Empire speaking Greek before the Empire even split?
I answered a similar question a few months ago - Why is it called the Byzantine Empire when the city was known as Constantinople for centuries longer than it was called Byzantium?
The very short answer is - there were anti-Greek sentiments in the medieval period (when the Empire still existed), and afterwards (when it no longer existed) that made western Europeans reluctant to admit that it was the Roman Empire. For them it was Greek and that was a negative thing. Then, in the 19th century, modern Greek nationalists looked to the medieval empire as their own glorious past, so for them it was Greek but in a positive way.