Ok...I finally see what's happening.
When you have 'Review Membership Requests' turned on and a new user registration is requested, that user is added to the Membership database, but it is not added to SharePoint yet. The users full name resides on the review list, it is not in the membership
database. The user management page displays all of the users in the membership database, whether they are in SharePoint or not - and since the full name isn't in the membership database, it just shows the username as the full name.
Once the user is approved on the membership review list, the user (including full name) is moved from the review list to a SharePoint group. Now the user and it's full name will be visible in the User Management page.
This is definitely a little confusing. The user does need to be added to the membership database, to prevent other users from registering the same user again. I'll look at adding the review data to the User Management page in a future release
to minimize the confusion.