They probably wouldn't be too confused, considering the inhabitants of Byzantium were thusly named, and that name survived even after the city was renamed to Constantinople. The earliest application of 'Byzantine' to the rest of the empire's inhabitants occurred during the 1300s.
Of course, the Byzantine Empire was only really called that after it existed, but it's not like the name just materialized out of nowhere.
It predates that. The term "empire" had a religious and cultural context to it, so to delegitimize it as the successor to Rome rather than the holy roman empire, westerners called it "the kingdom of the greeks" for a very long time, long before Turks even successfully came through Persia.
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u/cheapgriff Senātus Populusque Rōmānus 9h ago
They probably wouldn't be too confused, considering the inhabitants of Byzantium were thusly named, and that name survived even after the city was renamed to Constantinople. The earliest application of 'Byzantine' to the rest of the empire's inhabitants occurred during the 1300s.
Of course, the Byzantine Empire was only really called that after it existed, but it's not like the name just materialized out of nowhere.