Italic tribes such as the Samnites, Faliscans, Greeks, and Goths inhabited Italy before and during the Roman Empire, but eventually were folded into the empire and became completely Roman. How long did they hold on to their non-Roman ancestries, and when were they forgotten as they are today?
Follow up question. How was Roman citizenship proven? How could a poor urban pleb prove that he was an actual Roman citizen?
I can do the first part of this question.
Ok, first Goths were never Italian, at least in the period we're talking about (1st C CE or so). They were Germanics. They came 500 years later. Greeks.... Personally I would suggest the Italian Greeks should be considered Italian, but on linguistic grounds most people keep them apart. They are not considered "Italic" because their language isn't related to Latin in the way Oscan or Umbrian is - the split between Greek and Latin is further down the indo-european tree.
The collapse of Italian identities into Roman occurred sometime around and after the Social War of 91-88 BCE. There's controversy over why this war was fought and what it was fought for, but in the final settlement all of Italy became Roman citizens by law. So that's a terminus post quem. Ethnic identity continued to be an issue following this, such that Cicero developed a formula for Roman citizenship that described two fatherlands, one of affection, the local one where someone was born, and the political one, to whom one owed their political allegiance and their life if need be. For Cicero that was his home town in the the first case and Rome in the second.
Throughout this period ethnic origin continued to carry weight. We hear that Livy, for instance, had a certain "Patavinitas" that marked him as a provincial, although we don't know exactly what that accusation means. There are a number of names in Augustan Rome that derive from ethnics and presumably are meant to communicate the associated traits with those ethnics - such as Sabinus is a stoic guy, because Sabines were stoic, and so forth.
One of the emperors of 79 69 CE was Vitellius, which is "Mr. Italy" - and that's a pretty distinct ethnic marker if I have to make a guess.
After that, we leave my period and I hope someone can pick up the story from there. Maybe an Imperial historian can tell us about what happens after the Julio-Claudians.