(After all, its SF that's gone through a rough time, and been given over to Unselie by Hyperwave. QCO/QCP aren't the faction on life support here)
Then QCO and QCP need no name change.
HOWEVER, I am only one SF member. You should still do a poll to determine if the other SF members can live with the QCR solution. Change should never be rammed down peoples' throats.
Then assuming that most SF are ok with it, the way forward is clear.
1) All SF characters get names changes to QCR. (Queen Carina's Regulars) For instance, my character [SF]-SFF-Isaac.Brock becomes [QCR]-Isaac.Brock. (PLEASE ask admins if the NCC could be skipped, just for this case)
2) You change the faction status for QCO/QCP to "Queen Carina's Armed Forces" (Or something similar that suits Your Majesty), and update the Roster accordingly.