For a number of years, this worked.
Then all of a sudden I noticed that the name on my private account had been changed to GLENDA LARKE without my permission. Worse still, they had changed the privacy rating from 'friends only' to public. Also without permission. My private life was now open to all the world. Not that I actually I posted much up there that was private, but still.
I changed the privacy settings back again, changed the name back... And lo and behold, they reverted to what they thought it should be: Glenda Larke, public. This happened 3 times. I complained. Nobody bothered to answer. I attempted to delete my public page and leave the private one, but no, they have deleted them both.
So I am not longer on Facebook. (At least, I think so -- I can't look in order to check!)
I shall in time put up another author page, but I doubt that I will ever again post anything remotely private. This as far as I am concerned this was a betrayal of trust.