I cannot answer your question as completely as I would like to, but the idea that non-Romans comprised the bulk of recruits during Late Antiquity is incorrect. During the fourth century, it is estimated that (roughly speaking) only a quarter of field army recruits were foreign born. While the exact percentages are unclear (the Late Roman army being a poorly documented institution), the remaining three-quarters of field army recruits were men born inside the Empire. The evidence for limitanei units suggests a solidly domestic composition. Within the field armies, barbarians were not evenly distributed. They were typically concentrated into specific units (particularly foederati or auxilia palatina regiments) which were raised from barbarian prisoners or from specific non-Roman groups. This type of targeted recruitment was not a new development; during the Principate, many auxiliary units were raised from barbarian groups valued for their martial abilities (like the Batavians). Initially, units of foederati or auxilia palatina would have had a unique “ethnic character” (often reflected in their unit title), doubtless serving to reinforce cohesion. Over time, this “ethnic character” would have dissipated as casualties were replaced by local recruits. It is only after the loss of North Africa to the Vandals in the 430s that the Western army became comprised of independent barbarian groups, as the court in Ravenna could no longer afford to maintain the military system.

Much of the evidence for barbarian recruitment comes from names, which naturally do not reflect traditional forms. Yet Roman naming conventions were never static, and [continued to evolve during Late Antiquity] (https://www.reddit.com/r/AskHistorians/comments/46sepg/roman_names/d07mutr) (this link also helps to answer your question!). The Roman world was a cosmopolitan place which had long tolerated differing naming conventions. In regards to the army, there does not appear to have been significant pressure upon non-Romans to adopt new names or Romanize their existing one. Names themselves are often poor markers of ethnicity (and, therefore, of identity), as plenty of native-born Romans bore non-traditional names (such as Stilicho). Indeed, in the right conditions, even men who bore Roman names, like the Frankish magister militum Silvanus, might still not be viewed as Roman. When court machinations led Silvanus to be accused of treason against Constantius II, he considered seeking refuge amongst the Franks. Yet Ammianus records that a fellow soldier of Frankish origin counseled against this, saying that the Franks would view him as a Roman and likely kill him, even if his enemies at court viewed him as a Frank. The line between Roman and non-Roman was always a blurred one, especially during Late Antiquity. Names are only one of a number of factors that indicate identity.

In the Frankish Gaul, Romans tended to adopt "barbarian" names, but "barbarians" almost never adopted Roman ones. Thus, if you encounter a Roman name in the Merovingian period, you can be fairly sure that person came from a Roman family, but with a Germanic name, all bets are off.

The usual reference guide here is Förstemann's Altdeutches Nahmenbuch which has recently (by which I mean like in 1970) been updated and revised. I don't know of any English works; this is a stereotypically German area of study.