Well firstly, you don't have to give your real name! Or why not start a page for your book, chapbook, website or poetry night, story circle, etc. rather than one for yourself? I know friends who have had trouble from people they didn't want to be in touch with, but you don't have to get bogged down in all that.
Secondly, in Facebook terms 'fans' simply means that you're saying you like something. And the more you become a 'fan' of a magazine you think is quality or an arts organization that does work you're involved with or approve of, then the more you come up on their listings, and the more serious you look about your artform. Or the more well informed or even 'connected'. you appear. And they'll become 'friends' of yours too. This all is good for work and getting yourself known as a professional or a writer or whatever with a professional attitude.
Thirdly, Facebook is a vast networking resource - it's a way you can leave comments that might interest editors and other people you might want to know you're around, in you and hence perhaps your work. It has pages dedicated to listings of all kinds like poetry competition pages, and allsorts of special interest groups you might want to join and hear from or network with. It also means that, (because you can be in touch with people who you'd never have had the e-mail address for) you can have professional yet informal conversations with others about important issues which you would never have just e-mailed them about, with the Chat facility.
Like everything else on the web, Facebook is a resource, and if you don't want to get any of the downsides, just follow the protocols! It's like ignoring the online gambling ads when you go on YouTube! You can just watch a rare film you never thought to see again, OR click a gambling site and lose your house through gambling debts - I strongly recommend the former!
Check out Spoken/Written Bulletin S.W.'s Facebook page at;