Your display name is shown to other residents in your community, as a resident you have the ability to update the display name to whatever you prefer.
Community Admin users can see you full name as it is important for them to able to identify you accurately, as this information is only displayed to Admin users it is also only editable by them. If you full name is incorrect please see the following support article for details on how you can make a request to your Community Administrators to update your Full Name: Updating Full Name
To update your display name, click on View Profile on the bottom of the left navigation pane.
Click Edit Profile on the top right corner.
Enter your new display name in the Display Name field