In the ongoing saga of Facebook versus SL avatars, check out this NWN post, where we learn that LL suggests that instead of creating a Facebook account for your avatar, you create a Facebook page for your avatar (which you can only do from a Facebook account, which would presumably be that of your RL identity). You show up as the creator of the Facebook page, but only to yourself.
Facebook pages are typically set up for businesses, products, bands, celebrities/public figures, causes, and the like. They don't have messages associated with them, and can't have friends, and while Facebook accounts can "like" them, they can't "like" anything themselves. Your Facebook account is associated with the page as its creator, and as such, you, and anyone else you deem an administrator of the page, can see the list of creator/administrators.
I say to heck with Facebook; I don't want to go where I'm a second class citizen. I've taken the advice Strawberry Singh posted in a comment, and set up on 2nd Hub. At least, I've tried to. I misspelled my avatar's name, and it won't let me verify my account because of it. (If you go to the support page, they list as one of the most frequently asked questions "I signed up with the wrong email address, or I spelled my email or name wrong. What should I do?" That question links to the FAQ page, to a different question, whose answer basically says that if you didn't do any of those things, you can verify your account. Gee, thanks.) It's been eight hours since I submitted a ticket; we'll see what, if anything, happens.
So... if you decide to try 2nd Hub, for heaven's sake, double check your avatar name!
UPDATE: I was pretty impatient, wasn't I? Around 5 the next morning my time I got an email reply; the problem is fixed, and I'm now verified. More news as it happens.