For balance reasons you cannot have more then on Faction Companion (FC) at any time. Also if you repeatedly use a FC that belongs to one of your accepted faction enemies over time they will notice just like doing missions for that rival faction. Below I’m providing examples of what I think the FC’s could be for each faction.
Boomers: Boomer soldier armed with Grenade Launcher
Brotherhood of Steel: Paladin in T45 armor armed with a Tri Laser or a melee Paladin with a super sledge
Caesar’s Legion: Legion Recruit in recruit armor wielding machete or Legion Explorer in Explorer Armor armed with spears or maybe a hunting rifle.
Crimson Caravan: Caravan Guard in leather armor wielding a caravan shotgun
Powder Gangers: Powder Ganger in Powder Guard armor wielding dynamite. He would only chuck grenades so he would be weak up close.
Mr. House/Yes Man: Yes Securitron or Potectron.
King’s: King Member armed with .357 or a melee King with an unarmed weapon.
Gun Runners: Gun Runner Guard with a submachine gun or grenade rifle
Jacobstown: Super Mutant with a assault carbine or a Nightkin that will occasionally go into stealth and attack with a bumper sword
Silver Rush: Guard with Plasma Rifle or a Guard with a Laser RCW