I think I am missing something basic here. If you have a menu item that goes to a list, and you have a search on that page, and someone chooses a drop down field - 'Town' for example, with the names of the towns in the area as search options -
The results give you a list of profiles, but the same town name that was selected is shown in the list, and not the name of the users with that Town in their profile.

How do I get the results to be a list of user names that meet the search criteria for the field (other than username)?

You have to choose the fields you want the search to show toward the bottom, in the columns area of List Management. Also, the fields have to show in your profile.

I did. But I want the results to show the usernames, regardless of what field was searched.