Every person, business page and group on Facebook has a unique numeric ID. People can also have Facebook usernames that uniquely identify them. You can use either of these to access someone's Facebook profile.
Facebook ID Number to Name
Most of the time, you won't know your friends' Facebook IDs or their Facebook usernames as well as you know their real names. A Facebook ID is a random string of numbers, and a Facebook username isn't prominently displayed on the site. If you want to use Facebook to find a person, you usually search by name, not ID number.
However, if you have someone's ID number and want to map it to a profile, you can go to www.facebook.com/[id-number], replacing "id-number" with the person's Facebook ID. When you have access to the profile, you'll see the profile page including the person's name they used when registering with Facebook.
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This technique also works with a Facebook username.
Facebook Graph API
If you are a software developer, you can use Facebook's Graph API to do a Facebook ID lookup and find a person or something else on Facebook by its ID number. This may be useful if you need to automate the process or do it in bulk.
There are software packages available for popular programming languages like Python and PHP to connect to the Facebook Graph API.
You usually must have permission from Facebook to write code for the Facebook API. Consult the documentation for details on how to register and get permission to access particular API calls.
Use the "User" API endpoint to get information about a user using his or her Facebook ID.
Setting Your Facebook Username
If you want to have a custom identifier, such as one based on your name or nickname, appear in your Facebook profile URL instead of a random string of numbers, you can set this up by configuring your Facebook username.
To do this, click the down arrow button on any Facebook page and click "Settings." Within the Settings menu, click "Username." Type in your new username and, if prompted, re-enter your password. When you're done, click "Save Changes."
Your username can only consist of letters, numbers and periods. Uppercase and lowercase don't distinguish between usernames. Since lots of people can see your username, you want to avoid one that could be offensive. Only one person on Facebook can have each username.
You're not allowed to use a username that is designed to impersonate someone else, such as a celebrity.