They've mentioned around 10 at launch, with the potential for up to 20 at any one time, with the weakest occasionally being eclipsed and swapped out with rising powers like large minor factions. Here's who I think we will see.
SenatorDenton Patreus
EmperorHengist Duval (unless he is still in a coma)
Harold Duval
Princess Aisling Duval
Chancellor Anders Blaine
SenatorZemina Torval
Princess Arissa Lavigny
Federation
Federal PresidentJasmina Halsey
CongressmanZachary Hudson(Shadow President)
FederalAdmiral Vincent
Alliance of Independent Systems
Prime MinisterEdmund Mahon
Thargoids
Unknown
Minor Factions
Dukes of Mikunn
Crimson State Group
CODE? (The New Caribbean?)
Panem Farmers Association? (lol the potheads)
FD has said that "no minor faction is currently large enough to be a power" but I think that size wise, the Dukes of Mikunn definitely are, and lore wise, Crimson State Group definitely should be, they fought a full scale war with the Federation and arguably won.