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You can personalize your Facebook URL (web address) by selecting a unique username. It will appear in the location bar of your browser after “http://www.facebook.com/” when you view your profile. Starting at 12:01 a.m. (EDT) on Saturday, June 13, 2009, you will be able to select a username at http://www.facebook.com/username.

You can select a username that Facebook suggests or create your own. Select “Check availability” to check for available usernames. If the desired username is available, click “Confirm” in order to confirm your choice. Usernames can only contain alphanumeric characters (A-Z, 0-9) or a period (”.”). We’re looking at how we may potentially support non-romanized characters in the future. Once you have claimed a username by clicking the “Confirm” button after checking for a username’s availability, it is not possible to edit it, or to transfer your username to a different account on Facebook. Additionally, when an account is removed from the site, its username will not be made available. Facebook does this for security reasons.
You should make sure it is something you like and that it’s appropriate for friends, family, co-workers, and anyone else who might use it to find you.
Source: Facebook | Learn more about Facebook usernames.