As you have discovered, changing the name of a user account is only cosmetic; it doesn't change anything as far as the file system and Windows are concerned.
If you want to get rid of the old name completely, you need to follow the steps in the MS KB article,
How to copy data from a corrupted user profile to a new profile. That will make the new account with the new name into a clone of the old account. Although the account you want to clone isn't corrupt, the steps are the same.