You could write a series of books on this subject, it's extremely complicated, particularly considering Rome in one form or another existed for over 2,000 years. Keep in mind that while the general concepts of ethnicity and nationality have always existed, and the particular concept of "Roman" existed, the extremely bright lines of 19th/20th century nationalism did not exist at this time.

Different groups of people viewed themselves as more or less Roman over time, and were viewed as more or less Roman by residents of Rome or Latin speakers over time. Greek speakers in general probably would not have felt very Roman in 50 BC, but they probably would have felt pretty Roman in 250 AD, and extremely Roman in 500 AD.

Even within groups there were long periods of time where for example many Jews felt pretty Roman, but many other Jews were violently opposed to that. There were periods of time when many Germans were integral to Rome and had a Roman identity, while other Germans were hostile to Rome and clearly not Roman.

There were some nationalities in and around the empire that kept their distinctiveness, like Copts/Egyptians and Jews in the Empire, and Armenians and Bulgarians in and around the Empire.

There were other nationalities that mostly faded into general Roman identity. I doubt many people in 400 AD would consider their nationality Carthaginian/Punic for example, and places like France, Spain, and Croatia were pretty Romanized by that time too.