I’m in the process of changing my name. Which name should I use on Facebook?
You should use whichever first and last name you most identify with and use in everyday life. If you’re asked to confirm your name, you can submit something from Facebook ID list.
Keep in mind that you don’t need to have a government-issued ID to confirm your name. Facebook can accept combinations of things like a magazine subscription and a utility bill, or a piece of mail and a credit card statement.
Note: You can only change the name on your Facebook account once every 60 days.
Source: https://www.facebook.com/help/1090831264320592?helpref=hc_global_nav