Before the PP update, the greek factions had unique names for their parties, now they just have the generic "Disciples of Zeus, Disciples of Poseidon, etc." Some of these included:
Athenai (WoS) : Alkmeonid family, Philidae family, Populist party
Sparta: Agiads and Europontids
Boeotian league: The parties' name were based on the cities that were part of the league such as Thebai, Plataea, Orchomenos, etc.
Over the Alps perhaps!