There is currently no way to change factions from the selection that the program allots when you make a custom civ.  It has been said that it will preselect the same factions as the base regular civ you copied from.

I have asked for the ability to select factions as part of the Custom Civ setup and the Devs said they would add that ability in a future release.

I would add that if you're into digging into the XML files you might be able to find the faction file and make changes to your civ there, however I have no idea where those files are hidden