The majority of people that lived under the Byzantine Empire called themselves Romans.

The story behind the answer

True. The Byzantine Empire was the direct continuation of the Roman Empire in the East, and its people called themselves Rhomaioi—Romans. The state’s official name was the “Roman Empire” (Basileia Rhomaion), and emperors styled themselves “Emperors of the Romans.” The label “Byzantine” is a modern scholarly term, derived from Byzantium (the old name of Constantinople), and was not used by the empire’s inhabitants.

Though they largely spoke Greek and practiced Orthodox Christianity, their identity remained Roman in law, institutions, and political legitimacy. Even neighbors reflected this: Arabs called them al-Rum, and a Turkish polity was named the Sultanate of Rum. Memory tip: think of Constantinople as “New Rome”—as long as it stood (until 1453), the people who lived there believed Rome still lived, and so they called themselves Romans.