FB backlink wont help you on search engine (obvious)
FB fanpage NAMING will help you on search BUT you have to put spacing if it is for more than 1 word. (use periods)
The naming of your fb fanpage should get some good SERP, but you should backlink that whichever way you want.
And also, feel free to use generic names when naming your fan page, facebook does have their own search you know...