Custom category archive page needs to display multiple terms

Hi - not a GP thing, but I can't for the life of me figure this one out, so if anyone has a tip it would be most welcome.

I have a custom page for a specific custom category which was derived from archive.php. On this page I have a Search and Filter set of checkboxes which allows for a selection of one or more categories and the results are displayed below. This all works well.

I have a requirement to show the terms that were selected in a status line along with the number of results. It should show "10 works found for Category Name A, Category Name B". I've done the count, but I can't figure out how to do the term names.