In the upper right-hand corner, choose your avatar picture or user name.

Your profile page will be displayed:

Select the red Edit Profile Button. Your profile details will be shown, which includes your nickname.

In the Nickname field, enter your name as you would like it to be shown. It can be pretty much any variation you choose. Here are some examples:
P. Hansen, Peggy Hansen, Margaret Hansen, Hansen, Peggy’s Cat
Once the Nickname has been changed, Select the red Update Profile button.
After the profile has been successfully updated, in the field labeled Display Name Publicly As, choose the nickname as the choice to be displayed.
Choose Update Profile again, to save your choice.
Notice that your avatar name should have changed to the nickname. If it does not, try logging out and then logging in again.