You should be able to change the name under the user account icon in control panel. Instead of adding and removing the account, select “change an account” under the pick a task at the beginning screen. The next page will list the users on the computer, and you choose the one that you are looking to change.
This will lead you to a page that asks what you want to do. You may change name, password, picture and account type, remove a password, or set up a .NET passport.
Select change the account type first. An Administrator Account allows the user to create, change, and delete accounts, make system wide changes, and install programs and access all files on the drive. The limited account, the user is only allowed to change their own password, picture, theme, and other desktop settings, view files they created, and view files in the shared folder.
This explains why you are not able to change the name. Once you have changed the account type to administrator, you will be able to change the users name.