What I would try if I had the same problem:
-Login with the existing admin account
-In the system preferences, create your new user, give to the new account the "admin" permissions
-Login with the new user, and delete the old user (if the system preferences don't allow you to remove an account, I suppose you'll have to do that in NetInfo Manager)
But... you say that you like the way how things are set up now... creating a new account will reset everything for this new user... maybe you only want to change the name of the user (I don't know how to do that...)