I hate the word Byzantine

[Sarmatian]

Of course, there are some that disagreed with this term. The Slav neighbours (Bulgaria and probably Serbia) of the Empire often used the term "Greeks". The same term can be found in the West, which after Otto I had their own Emperors (yes, Charlemagne and his heirs also won the same title but the Imperial glory of that dynasty did not last very long).

In Serbia in middle ages, term "Romeji" (Romaioi) was used. Calling Roman Emperor in Constantinople a "Greek" was a good way to lose your head. Only the very last years of the Empire, when the Empire was even smaller then modern day Greece and was inhabited primarily by Greeks, hellenic heritage was accepted again.

I don't personally mind term Byzantine, as long as it is used to refer to the medieval Christian Eastern Roman Empire, not some imaginary country called Byzantium or even worse a Greek empire...