Arche Byzantiou is not wrong, but I'll tell you what's wrong here. You see, the word "Byzantion" wasn't used at that time. The Byzantine Greeks called themselves "Romaioi" (Romans) and their Empire "Imperium Romanorum" or "Autokratoria Romaion" in Greek. They still considered themselves descendants of the old Roman Empire, not a new Greek Empire. The Greek element just happened to be prevalent.
As for the capital, it's Konstantinoupolis (ΚΩΝΣΤΑΝΤΙΝΟΥΠΟΛΙΣ=Η ΤΟΥ ΚΩΝΣΤΑΝΤΙΝΟΥ ΠΟΛΙΣ or Constantine's city) in Greek.
Maion
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