Your public profile lives at /u/your-handle. When you became a host the handle was made for you - older accounts got the first part of their email address, newer ones their first name plus a number. You can change it any time in Settings → Profile → Public host profile: press Change, type a new one (3 to 30 lowercase letters or numbers) and we tell you straight away whether it is free.
One thing to know: the old link stops working the moment you save. Anyone who bookmarked it will see "Host not found", so share the new one after you change it.