The "Dominion of Soissons" was never called that way in their own times. Many historians believe there's something fishy about Syagrius and Soissons, and some believe it's a historiographical myth created by Gregory of Tours, who was writing the only History of the Franks that we have today, and who may have been very well crafting it.
Syagrius appears in this account as Rex Romanorum. King of the Romans. Some have theorised that the Limes and the Army were so culturally (not ethnically) germanised, that the whole "king" thing began to appeal to Romans, and that Syagrius, to oppose the King of the Franks, became the King of the Romans in Gaul.
Others say that Syagrius was just a Roman commander who fought Clovis and lost, and Gregory magnified this battle, raising the stakes and makign Syagrius more than he was.
Either way, "Dominatio" is not the word. You want "Dominium", which in Latin meant what now you call "Dominion", the part someone controls.
As for the several Roman Empires, I think they called them I. R. Pars Occidentalis and Pars Orientalis... But I'm not terribly sure. I have a friend who's an intern at the Department of Late Antiquity in my local university, I'll ask him.
Bad idea, I think. Rex Visigothorum was a real thing. Even Rex Gothorum, meaning Visigoths.