Obviously, most of these neighbors would be other "barbarian Kingdoms." Since we only have one names so far, I was to pick names that sound rather similar. Poking around a bit on Wikipedia, I end up getting the following names that sound decent for my purposes: Mercia, Bernicia, Cumbria, Styria, Silessia, and Moravia. They do sort of flow together, and I make me rethink some of my previous choices. What if "-ia" or "-cia" meant "land of" in the barbarian tongue? So instead of the conquerors being "Galcians" they are instead "Gals" or possibly "Galts" ("going Galt" in this world has an entirely different meaning than in ours.). Their language likewise wouldn't be "Galician" but rather "Galtic."
I rather like that, it's a but more guttural and harsh, which sounds better for a race of conquering warriors. I think I'm going to keep it.