Could we potentially see a dynamic geographic name for at least some of the states?
So if they hold their capital in, and the majority of, a particular region, that becomes their displayed name. So, holding Babylon and the surrounding area makes you "Babylon", but if you lose that and get driven into another region, your name changes to reflect the location of the new capital.
Dynastic naming could be a bit strange in some cases. I'm not sure I'd recognise a dynastically named Egypt under a native dynasty for example (and do we even have a name for those dynasties??).
Would a Greek kingdom be named for the dynasty of the king in question, or still named for the home city (or as some hyperbolic Kingdom/Empire of Hellas)?
Meanwhile what would the dynastic name be for the northern and western tribes (Gallic, German, British, Pictish, etc) if they managed to erect a strong kingdom? Or would they have to name themselves after the primary tribe/culture?
Would Rome always be Rome? Would it change to a dynastic name if it became a kingdom?
If it splits in a civil war, what would the part that doesn't hold Rome be called?
What if Rome loses Rome?
What if Rome loses Rome, and then Rome (the city) revolts free from whoever has conquered it, but doesn't rejoin the previous empire? Which gets to still be called Rome?