Don't know if they mandate it, but I know a few people who use either names that are a slight modification of their real name, or completely made up names.
How do they validate that? YouTube also wanted my full name before they finally switched back to usernames. I just made up a pseudonym back then.
Facebook has pretty advanced features that cross check your digital signatures like IP address, browser, registered email, etc to prevent sockpuppeting. This is especially true if you want to make ads with your account.