Ummm...there's an even simpler function to use.
MySQL supports MONTHNAME( ).
$query = "SELECT listing_name, MONTHNAME(start_date) as month_name "
. " FROM listings ORDER BY start_date";
Of course DATE_FORMAT works just as well. Just a bit harder to remember all the possible formats.
There's a couple of minor things I'd do differently than CFMaBiSmAd did, but his concepts are spot on.