Answer: If you are trying to change your name to just an initial (ie. from "John Doe" to "John D") The facebook terms now state that you must provide your full, real name in order to use the site (ie. no nicknames / initials). You may have seen previous accounts with initials, and that was because those accounts were created prior to this new rule, and apparantely Facebook decided to not bother those people (yet) with this rule.

If you have a name that is of a popular celebrity (eg. Luongo, Gretzky, Spears, Cyrus, Gomez) facebook may have blocked those names in order to reduce the number of fake profiles out there. If that is the case, you may have to contact facebook to get this resolved.