They called themselves the Roman Empire. It was only much, much later that historians tried to separate this period of the Roman Empire by calling it the Byzantine Empire. There is a bit of a resurgence under Justinian. He's able to capture significant portions of the West, including the Italian Peninsula. But then over time, the Byzantine Empire contracts. Especially in the East, it has to contend with the spread of Islam. As we go even further in time, as we enter into the second millennium, we can see that the Muslim Turks make further inroads into the Byzantine Empire.