One reason I went with 'union' is because it's already an occurance within rheinland - with the unioners. Unfortunately it's not as easy to base your name off something like that in bretonia since there really arent any...
Some more options-
Parliament maybe? Kinda tough to type in a hurry though. I still suggest basing it off of something western-european or bretonian.
Assembly
Senate
Council
Society
Corporation
Consort
Concordium
Guild
Conclave
Congregation
Convention
Corps
Those are all company or group synonyms, then you could add something based on the faction to it (like trafalgar or london or bretonian). Examples:
London Fence Society (fences are people who buy and resell stolen goods)
Trafalgar Concordium or Trafalgar Conclave
Bretonian Salvage Corps.
Leeds Congregation