I guess that this need to be random and not real hystorical names as rebels will repeat during game so you need to have several prepared names.
Maybe by rebel leader name, e.g. "Peter's faction", "Serbia (Peter's faction)" or "Peter's Serbia".
Or some attribute may be added like sides of the world, terrain types or geographical names e.g. "East Serbia", "Highlands of Serbia", "Serbia by Danube", ...
And once original faction is wiped out or diminished then rebel faction can be renamed to original name and former main faction can get name by leader/attribute (e.g. "Small <kingdom name>", "Old <kingdom name>",...). Of coure, if it is possible to script this.