That'll be considered the Byzantine Empire, after Byzantium, the former name of Constantinople. They called themselves the Roman Empire. Also a valid name for them is the Eastern Roman Empire, as that is what they were; the Roman Empire split into the East and the West.
Also, WHAT IN THE WORLD IS CONSTANTINOPLE DOING IN THE MIDDLE OF ANATOLIA!!! Constantinople is not in Anatolia, it's very close.
Finally, Why use that picture? That doesn't hold the extent of the Byzantine Empire at its greatest.