Whatever symbolic importance the city of Rome itself held, and still holds today, the city of Rome had ceased to be the political epicenter of the Roman world by the time we can start talking about a "Byzantine" empire. Even in the Western Empire, many functions of imperial governance were, as a practical matter, being undertaken from Milan or Ravenna. The Empire had ceased to be an Empire of the City of Rome and had become an Empire of the Romans. Even when the Eastern Empire asserted sovereignty over Italy under Justinian I, the seat of the Roman Exarch was in Ravenna, not in Rome, which continued to be dominated by the local Roman aristocracy and by the Popes.

In the later empire and into the Byzantine period, the empire's subjects - if we can even meaningfully call it an empire, but that's a separate discussion - appear to have conceived of it as a cosmopolitan whole. One of the watershed moments in all of this was the famous decree of the Emperor Caracalla in 212 AD extending Roman citizenship to free men throughout the empire. Beyond this point, Romans, Greeks, Britons, and Goths within the Empire's borders could lay claim to a certain kind of "Romanness." The mental boundaries of the Roman commonwealth extended not just to the city of Rome and its environs, but to the whole empire. By some point in the 4th century, and perhaps earlier, the term Romanía, or "Land of the Romans" came into usage in reference to the Roman polity. Anybody who was subject to Roman jurisdiction, in some sense, could be said to live in Rome. As Anthony Kaldellis puts it:

"The name could therefore be used in a purely internal frame of reference, not as a perception of the Roman world from the outside. Egyptian Christians, who were now Roman citizens whose religion was favored by the imperial court, knew that they lived in and were part of 'Romanland.'" (Kaldellis, Romanland, p. 86)

In this sense, territorial possession of the city of Rome itself was not a constitutive quality of Romanness. We even have good evidence that the people who lived under the Empire's rule in the Byzantine period considered themselves Romans, and distinguished themselves from non-Romans. Romanness was in some sense perceived as an ethnicity, and one could meaningfully talk about a Roman character and culture. Take another example cited in Kaldellis. The 9th century Emperor Basileios I populated a Roman colony in southern Italy with migrants from the coast of the Black Sea, which a Byzantine chronicler wrote was the cause of the persistence of Roman culture in the region. As Kaldellis notes, there are two implications here. First, that there were non-Romans in southern Italy, and second, that the lifeways of people living on the Black Sea coast under Roman rule were considered culturally Roman (Kaldellis, Romanland, p. 40). People who were Roman - ethnically, culturally, by the standards of the day - appear to have known that they were Roman, and the Roman Empire was their empire.

This Roman identity extended in other directions as well. Romans of the Eastern Empire knew that they spoke a form of Greek. This Greek was heavily influenced by Latin, especially in its spoken form, to the point that writing formal Greek required the self-conscious exclusion of Latin-inflected elements. We even have non-Byzantine sources attesting that the spoken, vernacular Greek was known as Romaic, or Roman. Evidence of spoken Greek being known as the "Roman" language exists even into the early part of the 19th century.

The territorial possession of the city of Rome does not appear to have been a priority for Roman subjects as far as their identity as Romans was concerned. The mental space of the Roman Empire, by the later imperial period, had far outgrown the Eternal City as a political entity. Even if they did not rule the seven hills of Rome, they were Romans because they had Roman culture, Roman customs, and spoke a Roman language.

Readings

Anthony Kaldellis, Romanland: Ethnicity and Empire in Byzantium

Anthony Kaldellis: The Byzantine Republic: People and Power in New Rome

Thomas F. X. Noble, The Republic of St. Peter: The Birth of the Papal State, 680 - 825