Fix:
Simply rename the user and modify the "full name" field in the user's profile. Windows uses a security identifier number "SID" which remains constant. This allows the new person to have the same desktop, my documents and other settings of the previous user.

Common mistake:
Generally, I've seen a new user get created on the server and configured on the workstation. After that, documents must be migrated from the old user's profile. Sometimes security priviliges cause problems too.
If you find yourself in this situation, my article on sharing profiles might help.