@ Maciamo, surely there will also have been some lucky ones who could have kept memory of its ancient-Roman predecessors even during the Middle Ages. Perhaps some aristocrats, but not even for the Colonna of Rome themselves, descendants of the Counts of Tusculum, who boasted an origin from the gens Julia, it was possible to document illustrious predecessors before the IX century. Many more - even among ordinary people - adopted new onomastic and cognominal strategies precisely between the end of antiquity and the early modern age. In my opinion, fixing on the persistence or not of names is useful to delineate some historical, social and cultural phenomena, but it can be a deadly pitfall to identify the ethnos of individuals or groups.
In the case of Italy, surnames are fixed and consolidated only after the relative provisions of the Council of Trento in 1564, when parish priests are obliged to keep careful note of baptisms in parish registers. In any case, it was a gradual process, if we think that in some rural areas the surnames were even fixed in the XIX century. Before the Tridentine Council and for at least a thousand years the situation of names was absolutely magmatic.
In many European countries, surnames are often patronymic forms. In Italy especially in northern and central Italy they end in "-i", derived from the genitive of a proper name or a nickname, or - according to a more recent theory - of the "plural" referred to and extended to the whole family group , always modeled on the name / nickname of a progenitor.
Now it is true that the choice of the proper name tends to mature in a precise ethnic context (in southern Italy no one would suddenly start baptizing a daughter "Dragana" instead of "Diletta", even if it has basically the same meaning). But let's talk about a situation extremely permeable to other influences and influences, even in a short time or a few generations.
The indigenous people of a region, almost always for reasons of prestige or for intent to assimilate towards their rulers, can assume relatively quickly non-native forms of proper names - and therefore in turn originate surnames with non-local roots. Already the "barbarians" assimilated in the ranks of Rome in the imperial and late ancient ages bore absolutely Latin and / or Romanized names. In the Gallo-Roman world and along all the current territories of continental Europe that you mention, belonging to the Roman Empire, I believe this was almost the norm. Flavius Victor, military general under Constantius II and Valens, was a Sarmatian; Aetius himself was perhaps of Gothic or Scythic stock for his father (who was still called Gaudentius!), and was only Roman / Italic for his mother.
Even the advent of Christianity has considerably renewed the heritage of onomastics, but the assumption of names of biblical-christian tradition, of apostles or prophets, does not immediately make their bearers or the surnames that derive from them Jewish or Middle Eastern.
Here too motivations of social prestige or religious devotion come into play, not infrequently combining among them: many Gothic priests of the Aryan clergy of Ravenna in the mid-sixth century have names of Jewish-Christian origin. In the same years, a lady in Como named Guntelda gave birth to a son called Basilius, a greek name like few others, perhaps exactly at the time when the Byzantines took power in Italy. But Basilius' son goes back to his name Guntio, probably because the Lombards were coming, and re-germanising the name could become more convenient. In essence, in the transition between late Antiquity and the early Middle Ages it is quite certain that whoever wore a Celtic or Germanic coinage name was not an ethnic Roman, while those who adopted Roman names could encrypt an extra-Italic origin, even a recent one (a phenomenon that continued for a long time : see again Bonifacius, Marquis of Tuscany in the middle of the 9th century, who was a Bavarian).
With the Lombards and the Franks arriving in Italy a little later, the Germanic onomastic system clears customs among us and for the same reasons, but inverse to the previous ones, the Italics who are gradually becoming Italian begin to assume names (and later surnames) of origin North European. Now the prestige comes from the new lords who came from the north, and obviously the phenomenon is more accentuated in the regions of the North and Center of the Peninsula, which were directly dominated by them. Italics with a Germanic patina, exactly like a few centuries earlier we found Celts and Germans somewhat latinized along the Rhine and Danubian limes of the Empire.
The fact that cognominal systems derived from the names of the ancient Romans persist in Central Italy doesn't surprise me: we are however talking about that area where the ethnic Romans were indigenous, so either by blood or by direct cultural irradiation it would have been impossible to supplant completely the local onomastic tradition, however courtly. (It may also be the case that we are talking about families of humble origin, but whose ancestors found themselves in the service of landowners and gentlemen from whom they borrowed the name ...).
Other times things get even more complicated. Keep in mind that sometimes the maternal line is the one that has the pre-eminence and can change the name / surname of the family irreversibly, also here almost always for reasons of greater social prestige. Our greatest poet, Dante, in the "Divine Comedy" often made reference and pride to the Roman ancestry of Florentines like him. He was a descendant by paternal line from a Tuscan / Central-Italian aristocratic family, the Elisei, but Dante's great-great-grandfather, Cacciaguida, married a lady from an equally and perhaps even more illustrious family, that one of the "Aldighieri", originally from the Po Valley, from which the descendants then took the surname. Here is another Germanic surname, which is not said to be a spy of authentic Nordic roots, for the same reasons mentioned above.
I don't want to go too far, I haven't focused on other numerous categories of surnames that have imposed themselves over the centuries. Anything is possible in this world, but thinking that ancient names and surnames may have been handed down completely unscathed without considering the heavy and complex medieval passage is at least very risky. I attach a small contribution (in Italian) by Carla Marcato who teaches at the Udine University to give an idea of the extraordinary complexity of this phenomenon
https://edizionicafoscari.unive.it/...xNAeyhZD0Lax9nI_t_WRG6Rir48VxdraipzAl8AsWn5Gk