Why did Byzantine inhabitants call themselves Romans?

Inhabitants of the Byzantine Empire referred to themselves as Romaioi, or Romans, because they viewed their state as the direct continuation of the Roman Empire.1

They took great pride in their Roman and Christian heritage, believing their empire was founded by divine grace to unify God's people. Because they perceived their earthly state as a reflection of a heavenly pattern, they considered it an eternal institution that could never change. The term "Byzantine" was not used by the inhabitants themselves; it was a later designation applied by historians to distinguish the medieval eastern state from the earlier Roman Empire, as the society and administration evolved significantly after the 7th century.1

While they identified as Romans for most of the empire's history, a more self-conscious Greek identity began to emerge in the 12th century, eventually leading some to identify as Hellenes as the empire neared its end.2