To change the display name on your WordPress site so it appears as you and not your username, Go to Users > My Profile > Display Name.
Type in your new name.
Why the Display Name is Important
The Display Name in WordPress is also known as the byline. It is your name, your identity, that appears on posts and Pages in the post meta data section featuring your byline.
Your byline is your identity. It is your author name. While you may wish to be anonymous, having a human sounding name is better than some cute CB radio handle or nickname. It’s professional, and makes people trust you.
There is also a security element. If your username is displayed as your byline, you’ve given someone a piece of the security information to login or attempt to hack into your site.
Changing your display name in WordPress is a simple thing to do, and should probably be a part of the registration process since it should be the first thing you do on your new site. Once done, it is done forever on your site.