Click on the icon of your Avatar in the top-left corner of the game (marked in red in Image 1).

A window will open where you can view and edit your Avatar.
In the lower middle of the Avatar window, you’ll see your combined name (shown in Image 2).

This combined name consists of:
Nickname (highlighted in orange)
Handle (highlighted in green)
Both are separated by a # like this:
Nickname#Handle
A flexible in-game name
Not unique (other players can have the same nickname)
Can be changed from the beginning
A unique name
Used to find friends or let friends find you
Can only be changed after completing at least one full round on a game world
In the Avatar window, click the edit icon (highlighted in yellow in Image 2).
A rename window will open where you can edit your Nick- and Handlename.

Once you have entered the new names, click Confirm to apply them.