Ok so I went into the %appdata% file and edited mod organizer.ini, changing
gameName=Fallout 4
gamePath=C:\\SteamLibrary\\steamapps\\common\\Fallout 4
to
gameName=Skyrim
gamePath=C:\\SteamLibrary\\steamapps\\common\\Skyrim
but that only changed the Fallout 4 profile to read the game as skyrim. I changed one, changed it back, and then changed the other, and afterwards the only thing it did was change my fallout 4 profile to be skyrim, and leave the broken one as fallout 4. And the fallout 4 profile is now permanently labeled skyrim. I can't figure out how to delete the bad profile, or rename the good one.