I've never used an awt.List before, but I can make a suggestion based on the API.
There isn't a constructor for the list that allows you to give it a pre-sorted list, but instead you'd have to use .add(
String item, int index)
Doing it this way, you'd need to ensure that every time you go to insert a name, that you are inserting it in the right place. Sort of like linked lists. You could use the getItems() which returns an array of Strings. Then you can compare each String in that array with the String you want to insert. As soon as you find that the current array String (at [index]) is alphabetically 'after' the one you want to insert.. then use [index - 1] as the parameter to the add method like: .add(String nameToInsert, int index -1)
Something I just thought of... the API doesn't specify if the item that is currently at that index gets removed, or if everything bumps down one (like in a Vector). If it doesn't get bumped down, then you will need to implement this bump-down behaviour yourself.