It is a very interesting question and has a curious answer: in fact, the inhabitants of the Italian peninsula stopped feeling Roman long before they started feeling Italian.

The first Germanic people to successfully establish stable rule over Italy were the Goths led by their king Theodoric the Great in 493. Goth Italy was a very clearly divided Italy. On one side were the Goths of the Arian faith who made up the bulk of Italy's army. On the other there are still the Romans who occupy almost all civil offices and the Catholic clergy. In addition, Goth Italy was officially an imperial province belonging to the empire of Constantinople, whose administration and defence was entrusted to the Goth king. In the eyes of a Roman citizen, Italy at the beginning of the sixth century was not very different from Italy at the beginning of the fifth century, despite the supposed fall of the Western Roman Empire in between (there would be much to discuss): fanciful games and executions in the circus, the Senate with its wealthy landowners, coins with the emperor's face, the elaborate Roman bureaucracy, aqueducts supplying water to public baths, and a bunch of imperial troops of Germanic origin roaming around.

Roman Italy really died half a century after the arrival of the Goths, when the eastern emperor Justinian preferred to have direct control over the province and invaded it. Italy was completely devastated by a war that lasted for twenty years between Eastern Romans and Goths, with the Romans of Italy in between. The Roman senatorial class, rich and influential before the war, sided with Constantinople and disappeared completely: many were killed by the Goths in revenge, many fled to the East and stayed there. Famine and plague epidemics depopulated cities and countryside. The aqueducts of Rome and many large cities were destroyed in the sieges.

The war was finally won by the Eastern Romans, but just fifteen years after the end of hostilities with the Goths they had to face and this time lose another war: that with the Lombards of King Alboin, another Germanic people. Unlike Theodoric's arrival in Italy, authorised and legitimised by the Eastern Emperor, Alboin crossed the Alps in open warfare with the empire and once he had conquered a large part of the peninsula he owed no obedience to Constantinople. The Eastern Romans only retained control of parts of Italy: the large islands, the imperial capitals Rome and Ravenna and other narrow coastal areas.

Now, let us put ourselves in the shoes of a Roman citizen in early seventh-century Italy, a century and a half after the historiographical end of the Western Roman Empire. He still feels Roman, but there is not much to be proud of anymore. Senate? Not there anymore. The emperor? Far away and probably unable to return. The legions? Defeated. The Roman lifestyle of amphitheaters and baths? Stuff of the last century. Plus, there is a "Romania" in Italy, a land controlled by the Romans and subject to the laws of New Rome (i.e., Constantinople). Only it is not the one he lives in: it is the one controlled by the Eastern Empire. Which moreover includes Rome itself. From which also military expeditions sometimes depart against the place where he lives.

Slowly, the Roman citizens of Lombard Italy (which included almost all of mainland Italy) began to admire the new Germanic ruling class. The Lombards were the only truly free men on the peninsula, the only ones allowed to bear arms and serve in the army, the only ones who okay, occasionally plundered the countryside, but also defended it from arrivals of Franks or Bavarians or Saracens or from the Eastern Romans themselves ... and they had even by then become Catholics! In short, over the course of the two centuries of Lombard Italy those who had previously been Roman became more and more integrated into the new ruling class, adopting their names such as Ildebrand or Aliprand and feeling like they were Lombards.

When Charlemagne defeated Desiderius in 774 and ended the Lombard kingdom, he assumed for himself the title Rex Longobardorum, king of the Lombards. Only a few decades later did the term Rex Italie, king of Italy, come back into vogue. The inhabitants of Italy began to feel Italian in the middle centuries of the Middle Ages.