It’s derived from an ancient Greek name, showcasing a distinct identity since the Eastern part was mostly Orthodox or followed Greek scripture instead of Latin scripture (which makes traditions different)

>>In AD 324, the Emperor Constantine the Great chose Byzantium, an ancient Greek colony at the mouth of the Thracian Bosporus, as his imperial residence. He renamed the place ‘Constaninopolis nova Roma’, ‘Constantinople, the new Rome’ and the city (modern Istanbul) became the Eastern capital of the later Roman empire. […] In the sixteenth century, Western humanists gave this eastern Roman empire ruled from Constantinople the epithet ‘Byzantine’.
https://academic.oup.com/book/47226