The name Rûm or Roman was given to the five ancient apostolic sees (Jerusalem, Antioch, Alexandria, Constantinople, and Rome), which were the great administrative and spiritual centers of the Byzantine Roman Empire. It does not imply necessary that the congregations of these Churches were Romans or Greek, rather it implies that, in spite of these congregations' various ethnicities, they followed the faith of the Byzantine Roman Empire Universal Church.
Historic books, including Arab ones, referred to the 'Romans' of the eastern part of the Byzantine Roman Empire as 'Rûm', in order to distinguish them from the 'Romans' of the western part of the Empire. Meanwhile, the western ones called the eastern ones 'Greek', and later Byzantines, in order to strip them from the Roman belonging and keep it for themselves. While in fact, it was the western ones who were stripped from this belonging after being occupied by the German tribes (Visigoths, Ostrogoths, Vandals, Burgundians, Lombards, Franks), where the Roman culture disappeared, and they were divided from the eastern part of the Roman Empire, hence away from the source of the apostolic theological paradosis.
The term 'Rûm' does not imply an ethnical belonging, rather a cultural one, and a stamp of originality. Romanism was the environment in which the Church got its first cultural and civilizational character, where the Church' saints, holy fathers, professional poets and artists used the linguistic expressions, philosophic terms, poetic origins, and figurative music that were common in that culture. This environment was also enriched by the various cultures under the Byzantine Roman Empire, such us the Greek, Roman, Aramaic, Egyptian .. etc.