What would a fake facebook account achieve?
I don't get it..
You can think of it as a single-purpose pseudonymous account. That 'single-purpose' can be whatever you want it to be. For example, you could have the name Dee Lordio or Dar K Lordio or something else vaguely resembling a real name. The point is to be able to access the features of FB, especially the 'friend' networking part; often, you use it to promote something you want to promote, whether it's an idea, a point of view, cat photos, a WL clan, or whatever. Think of it kinda like a blog in a way. People who 'friend' you get updates about stuff you post, like notices, etc. You can also use it as a generic platform for discussions or chats.
I have used such pseudonyms in the past. I kept all my personal info 100% out of it. The only thing they could really track on me would be my IP address (too lazy to bother working around that, but if you're concerned about even that, you can easily hide it), and whatever associations I generated as a user under my single-purpose persona/alter-ego (such as topics ('likes') and other FB accounts (real or pseudonymous)). The only 'friends' I kept were people who openly shared the same interest in the topic my single-purpose alter-ego was interested in and promoting. It really is quite analogous to a blog network in a lot of ways, but much more interconnected and amorphous.