Right click on your sovereign in the selection screen.

for sovereigns go under: /documents/my games/fallenenchantress/units (right click on the sovereign works in removing the sovereign from the screen. The file is still available in this folder though.

for factions go under: /documents/my games/fallenenchantress/race

There is no mis-information from my reply.

If you do use right-click it does remove the character from the sovereign choices screen.

But the file is still in documents/my games/fallenenchantress/units

That file didn't get deleted and if you create 100 sovereigns that folder can get cluttered. Go check it out yourself.

Also, if you create a custom faction and you wish to delete the faction you need to go to

documents/my games/fallenenchantress/race

and that is currently the only way to remove factions.