How to force Active Directory to update users name?

In the user list, select the user, right-click and select Rename.

There are actually 6 fields that control user's name and username, and the only way in GUI to ensure you change them all is to do what Patrick and Vick Vega suggests. Just opening a user's properties and changing things doesn't cover it all. Always better to F2 or r-click->rename in user list to see all the fields.

The key is that Full Name and Display Name are different fields, but not obvious until you have this issue :)