Overall, elites in western Romania were issued from both Roman nobility and elites, and from Barbarian leadership and truste.

It doesn't mean that things remained unchanged after the collapse of the Roman state : after all it is the very existence of this state whom depended the power of this Roman nobility and not just land ownership. Furthermore, the damages due to foraging,plunder, fiscal or land requisition by Barbarians had their social consequences for a significant part of the Roman elite, while promoting the rise of a Barbarian leadership gathered around their royal lines.

A first consideration is the establishment of Barbarian states in replacement of the imperial Roman state during the Vth century ; collapsing, unable to maintain its militia (its military and civil service which were increasingly confused since decades) beyond Italy, the Roman state let the western provinces fall into warlordism, either Barbarian (Goths, Burgundians, Alan, etc.) or Roman (Aegidius, Paulus, Riothamus, Marcellinus, Victorius, etc.) it ended up that the only way for local elites (senatorial, military, etc.) to either keep their social ambitions and functions, and to maintain a territorial power obtained trough the Vth century, was to resort to palatial service where it existed, meaning the Barbarian states.
It wasn't a matter of simple submission to new masters, tough, but rather meeting the needs of the kings emulating their state after the late imperial features with their social and cultural ambitions.
Depending from kingdom to kingdom (Goths keeping much of the forms of late imperial state and administration, Franks initially having only a barebone militia, Burgondians attempting some administrative experiments) it was mixed with the power and opportunities tied with the proximity with the king and the royal court, which was a way to obtain (or legitimize) a non-formal or administrative power.

The old imperial militia wasn't reborn from the ashes, tough, but more territorialized (both in terms of scope and in terms of gain, as landed revenues replaced waged service), which tended to accelerate the confusion with the elites who beneficed from land ownership (rather than just enjoying its products or benefits). Again depending from the political situation, capacity of redistribution and importance of localism; the confusion between an aristocracy "by birth and proximity" and an aristocracy "of service" became less clear (especially in the peripheries at first, the roman model surviving more or less until the VIIIth century).

In the end, the confusion was more or less achieved during the rise of Carolingians (who represent both trough their rise and trough their takeover, a triumph of this situation and confusion of service, honors and landed benefices), who attempted to mix all that in a new concept of militia, which utterly failed into feudal anarchy.

But by the VIIth, the distinction between Romans and Barbarians was moot or on the verge being so, as most of the elites acknowledged themselves as Frankish, Gothic or Lombard (with the noted exceptions of Romans in Aquitaine, for example, which weren't really different from Franks in these matters, tough) : a line of Roman nobles could adopt Frankish names quite easily (we have the example of a line of people named Lupus whom a member decided to adopt a new one, "Wulf"). Most of Barbarian nobility by then was culturally Roman, either by origin, either because of an heavily romanized Barbarian origin (and this from the IVth century onward).

The case is a bit different with Anglo-Saxon nobility : most of the familial origins are legendary and re-made a posteriori, but it's quite possible that there was a mix with Britto-Roman families (for instance, the initial kings of the House of Wessex bearing Celtic names). But the Norman invasion essentially rooted them down in the XIth century.

We can't really attribute late ancient or early medieval ancestry to classical or late medieval dynasties : it's not as much that records weren't taken than a good part was lost (due to material fragility, neglect or sheer destruction) but that there was a nobility rupture in the late and post Carolingian period, in term of political continuity. Even the early medieval origins of extremely prestigious lines such as Robertians-Capetians can only be proposed trough onomastics (for all we know, their founder might have been a Roman noble whom descendent took a Germanic-sounding name), Habsburgs attempted to trace their familial origin up to Etichonids but it is not necessarily this direct (or truth to be told, that convincing) and while some regional dynasties attempted to tie themselves to famous ancient families, it tended to loose in credibility what it gained in imagination.