I haven't had a Facebook account for a few years.
I agree with going Secret for now as a least-possible-damage quick fix until we've had a chance to discuss.
I also prefer Secret for the long term, because (a) the facebook group is an auxiliary to the board and not a general-purpose Buffy discussion group, and I can easily imagine a future where a ton of people come in that way and the fb _loses_ the usefulness it currently has for "is the board down" and "hey, if you haven't checked in for a while, please check Beep Me", and (b) facebook is a motherfucking cesspool of toxicity and actual evil, perhaps even a hellmouth, so I'd rather not see it become a primary discussion place with a whole different but overlapping crew of people (however lovely they may be).
I think amyth is right.
Not to mention, most people use some iteration of their real-life names on FB (including most Buffistas). While Buffistas aren't really a group where you see a lot of usernames of the Elmo_Pelt79 ilk, most people are less identifiable here, than over there.
I don't really know where I was going with that, except if I still had FB, I'd be fine with people who got to know me as Topic!Cindy over here, figuring out that in actuality, I'm really international supermodel Cindy Crawford.
But I wouldn't necessarily want everyone who follows me, international supermodel Cindy Crawford, to track me to B.org.