Yes, I would change the specific SQL user login to match the person's name, if all/part of the name itself is being used as part of the login.
Use roles, where possible, to assign permissions to logins, as that will simplify management of permissions.
Have a script that "converts" the old login to the new login.
SQL DBA,SQL Server MVP(07, 08, 09) A socialist is someone who will give you the shirt off *someone else's* back.