How were the names Byzantine and Byzantium coined?

by Zand731
Lele_

The city was founded in the VII century B.C. by Megarese colonists with the name of Βυζάντιον (Byzántion). The etymology is unknown, though the legend makes it derive from the name of one king Byzas (Βύζας) of Thrace. Byzantium is the latinization of the Greek name, substituting the neuter gender -um ending to the Greek one, as was usual.

Byzantine as an adjective was never used by the Eastern Roman Empire to refer to itself, they used Ῥωμαῖοι (Rhōmaîoi, meaning Romans) or Γραικοί (Graikoí, meaning people of Greek culture) or even Ἕλληνες (Hellenes, meaning Greeks again but more like the ethnonym of people born in Greece) depending on the context and period.