I mean things like country. So far I have: Caliphate Dominion Republic Kingdom Empire State Federation
These have all historically been used to describe independent states: Commonwealth Principality Grand Duchy County, or Countcy Exarchate Palatinate Khanate Sultanate Emirate Despotate Confederacy These have not, but they could exist as theocracies: Bishopric/Diocese Archbishopric/Archdiocese
Get yourself a world menu. It's like a dictionary, except the words are organized by subject matter instead of the alphabet. Here, hold on a sec..... Township, exurb, burgh, metropolis... Monarchy, coalition, aristocracy, isocracy, gerontocracy, principality, straococracy, technocracy, triarchy... Commonwealth, municipality, triumvirate... I guess that's all I've got.
Or, just "United" any of the above (sometimes plural) The United Dominions for example The United Grand Duchy
I like the city-state idea. City-state of London Baby! Aka just the name of the city, but say it's a city-state, like Vatican City and Singapore do... Which are also countries/country cities! (yay)!
When I was in the military in Texas a young man (shoe-shine boy) said, "I'll bet you fifty cents I can guess what state you were born." I said, "You're on." He said, "State of infancy." I paid.
May need some context here. Most of the time, states are named after their government forms. That sort-of leaves an almost endless possibilities. From as simple as a "Republic of X" to frivolous stuff like "Reformed Agrarian Grand Princessity of X". The above note also shows one easy way to go is to look at who's ruling a state. If it's a duke, it'll be a Duchy. If it's an Archduke, then it'll be an Archduchy. If it's a Celestial Princess - Celestial Princessity. Can go on with Baronies, Earldoms, Counties, Marchdoms, Marquisdoms, Landgraviates, Palatinates, Burgraviates, Duchies, Principalities, Archduchies, Grand Duchies, Princessities, Kingdoms, Queendoms, Empires, Patriarchates, Matriarchates, Sultanates, Caliphates.