Your short user name is both your account name and the name of your home folder. You can’t really change it. But you can create a new user account and move everything to that account if you are willing to put a lot of effort into it.
Related: Standard user and Admin User, Create a new user, Root User, MacMost Now 336: User Accounts and Fast User Switching, Safari application not showing in new User Account !.

Hi Gary… Thanks for all of the great videos.
I’ve got five Macs and thought I would try the the Apple instructions using the root user that you mentioned in your video. I couldn’t get it to work on a new Macbook Air running Lion. Admittedly, I was a little nervous so I aborted at the first sign of a problem, even though I had a clone and Time Machine backup of the drive.
Instead, I created an alias via Login Options-Advanced that appears to have accomplished my goal. My goal was to be able to move to any of my Macs (via network or physical presence) and type in a consistent administrators name each time the Mac requested it when installing software, etc.
(I think the root user method may not have worked because my short name on the Lion machine was not all in small case letters, something that I migrated to the MacBook Air (which is why I wanted to change my short name), but who knows.)