If we were to seach through most European language families, we would find "loan words' which have been "borrowed" from other langauges.
Originally, I would think that the most proliferate would probably have been Latin and Greek. In Europe, those langauges would also have originated from the Angles, Saxons, Jutes, the Norsemen.
In more recent years, asian loan words have been increasingly adopted.
So, to say that particula people or groups of people are/are not Roman is an oversimplification of the situation. No doubt there are people throughout Europe and North African whose DNA can be traced back to a Roman intervention. But, I submit, they are not Roman.
The Romans are not even resident throughout modern Italy, IMHO, they are the people who live in the city of Roman.
Would an English migrant to the USA still be regarded as being English? Unfortunately, probably, but that's due to bias against the English, based on centuries old conflicts.