Simple. At the top right corner of your FB account, click on the >>> small arrow, then click >>> Account settings, scroll down to >>> Username and then click >>> Edit, change, add password and BAM!!! .... you're done.
One thing you should always remember is your FB user ID. Here is an article on how to find Facebook user ID which can be helpful to you.
To change your username: Open the Account dropdown menu at the top right corner of Facebook and choose Account Settings. Click the Edit link next to Username. Type your new username in the open field and click Save Changes.
You can change your "username" only two times. Simply login then account setting >> username . If u selecting username first time then u must verify your mobile number to complete this process. Second time u can change it easily Facebook will warn that u can change username only two times. Thanks.
Now u can also select a username for your facebook page. For a page you must have minimum 25 likes to get a username. Edit page >> username