Yes, Facebook joins with twitter via free to change the user id or custom URL of user profile. In past Facebook allowed to change the user name of profile few times or locked after three changes of edits. and now Facebook joins with twitter and allowed to change freely, multiple times you can edit the user name of your profile or fan page name and user ID.
we already know in Google Plus, locks the email id and custom URL. the both we cant change still now. but in Facebook we can change the email ids and now allowed to change custom URL of your profile user id.