Hi, Whiskey_Sierra
You are right, the Empire has disappeared, it was just the most simple "cheat", in my opinion
Suggestions...
RED
For 1918-1922 - Soviet Russia (red in the game and Red in history) is a proper and common name. It's easier than abbreviations such as RSFSR or else, there were several of them in the short period.
Since 1923 - USSR.
Other numerous Red/pro-Communist factions are not important, probably, since they hardly had any aviation or have been just Soviet Russia's proxies.
BLUE
1917 Mar to Nov - Russian Republic or Russian Provisional Government.
1918-1922 - several "White" governments, proto-states and armed forces in different regions. Probably, White Army is the most simple name for the game to identify all of them.
Then there were new independent states with some aviation, but probably all included in your list already. Central Asia is a grey area but the air war there was one-sided (by Red Army).
Don't hesitate to ask if you need advice on anything related to that period and that region.