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) "It's a dog-eat-dog world, and I'm wearing Milk-Bone underwear." "Norm", on "Cheers". Also from "Cheers", from "Carla": "You need to know 3 things about Tortelli men: Tortelli men draw women like flies; Tortelli men treat women like flies; Tortelli men's brains are in their flies".