Remember your Facebook profile also. People volunteer birthday, who they are married to, career, friend list, high school class, entities liked, etc.
All that can be extracted by marketing companies via a web crawler.
Sure, you can adjust privacy settings but would you trust FB?
Subterfuge is better. Change your birthday, city, middle name for example.
It's kind of strange logging into Facebook (under a completely fake identity) and getting a "Happy Birthday" announcement on some random day that isn't anywhere close to my real birthday. LOL.