I changed mine, by first deactivating my old account... but when I went to reactivate it with the new username, the system would not let me use the same email. After contacting support, the solution ended up being:
1 - Fiverr reactivated the my old account (with same username, nothing changed)
2 - I changed my email address (which you can do easily).
3 - Then deactivated my account again.
4 - Initiated a NEW account with my old email (not the one I changed it to), plus a new, and better Username.
That worked for me.
Best of luck.