The full name in your edX account is the name that is used for certificates. At any time, you can change your full name in your account settings. After you change your name in your account, any certificates you have earned will automatically update to reflect the change*.
For step by step instructions for updating your name in your edX account, please review How do I change my name on my account?
*Unfortunately we are no longer able to update older PDF certificates earned before October 2015.