I think most agree that a foreign overlord who conquered Rome would at least have considered the idea of recruiting natives in their own fighting style.
Would they have used Roman military jargon to designate these units? I'd guess not. So it's down to the name.
"Latin infantry" (translated) seems suitably generic for a unit recruitable to factions like Karthadast, Epeiros, etc. But as mentioned many of Rome's non-Latin allies fough in the same manner..."Italian infantry" (again, translated) would be an alternative, but that's too generic IMO.
Maybe something like foederati legionarii, but I feel like I'm stretching here and my latin skilz suck...