Go to your profile settings page on geocaching.com. The "user name" block is just below the two profile photo area.
You can only change to a username that is not in use.
Also, from the Help Center, there are some restrictions on user names that didn't always apply, so your choice may be limited:
Usernames must be between 2 and 20 characters. Geocaching.com supports the following characters for usernames; all other characters, including spaces, are invalid:
- a to z
- A to Z
- 0 to 9
- ä ö ü ë ï ÿ æ œ ß á é í ó ú ý à è ì ò ù â ê î ô û ç ñ å ů č ě ň ř š ž ť ø ď