Why is the Eastern Roman Emperor also called the Byzantine Empire?

Constantinople, the capital of the Eastern Roman Empire, was originally a Byzantine city of ancient Greek immigrants, so people also called the Eastern Roman Empire Byzantine Empire. This empire spans three continents: Europe, Asia and Africa, and its ruling areas include the Balkans in Europe, Asia Minor in Asia, Armenia and Syria. Palestine, the upper reaches of Mesopotamia, and vast fertile areas such as Egypt and Libya in Africa.