Ethnicities change and evolve over time. During the classical Roman Empire "Roman" in some contexts might have been considered an ethnicity or a nationality, depending on the context, time, and even individual, similar to perhaps the term "British" today. There are people who consider themselves ethnically British, British people who consider themselves ethnically English/Scots/Welsh, or British citizens who are ethnically, say, Japanese.

There were Roman citizens who had no other ethnicity than Roman, or Roman citizens who were Jewish or Greek or Egyptian. One important development was that during the late classical Roman Empire the ethnicity "Greek" gradually disappeared, and Greek first language Roman citizens became just "Roman".

During and after the end of the Roman Empire, Germans increasingly entered Italy and took military leadership roles, initially alongside Romans, but after the Lombard invasion, the German ruling class was clearly in the dominant position.

The Greek Speaking Eastern Roman Empire still existed in the Middle Ages, and the advent of Islam forced a re-conception of "Roman" identity among the population of the Roman Empire. Christian inhabitants of the Empire (with the partial exception of Armenians, who practice a distinct form of Christianity) basically all adopted a "Roman" identity. You don't hear of "Isaurians" or other historical ethnic groups of Asia Minor anymore in the Middle Ages.

Italy during this time period kept getting invaded by new groups from the South (Arabs and Normans) who ultimately totally displaced the Eastern Romans out of Southern Italy, and continued to be entangled with Germany. The relationship between the powers in Italy with the Roman Empire became increasingly distant and hostile, and the schism between the Latin (Catholic) and Eastern Orthodox churches, followed by the Fourth Crusade where Latin Christians attacked and occupied Byzantium accelerated this.

When the Ottomans took over the Roman Empire, they 1) Started calling themselves the "Sultanate of Rum" (Rome) 2) Referred to their Orthodox Christian subjects as the "Rum Millet" (Roman nation).

Greek speaking Ottoman subjects continued to consider themselves "Roman" until at least the advent of Greek nationalism in the early 19th century. There's even an unverifiable story floating around about the post WW1 incorporation of formerly Ottoman territories into Greece where some Greek speaking locals continue to consider their ethnicity "Roman".

In summary, between 500AD-1800AD the world contained a "Roman" ethnic group that had a limited connection to Italy, meanwhile Italy went through a ton of changes including an imported elite that wasn't really connected to the historical Roman Empire.