Hi,
After you change the user's name in the Domino Administrator, Unity should detect the change, and make the update to SQL automatically. So when you open the Unity System Administrator (SA), you should see the name change. The Unity service that polls for changes is DSDomino. I don't recall the polling interval for sure, (I think it's 3 minutes), but within 5 or 10 minutes you should see the change in the Unity SA.
Nancy