There should be a way to distinguish between the factions of the same type. I like the idea of creating a civil war senario, but the faction power box would be all but useless. I recommend adding the sovereign name to distinguish between the factions. Another option is to allow the player to write their own faction names in game for each of the players.

Even if I had created a custom faction other than the one I was playing, which I hadn't, wouldn't the second custom faction be using the custom sovereign I'd assigned to it?  

This was two canon sovereigns, one from Altar and one from Pariden, each leading a separate Altarian faction.  FWIW, I have not run into Procipinee leading Pariden properly yet on that map even though Pariden was supposed to be in the game.  I'm about 2/3 of the way across the map.