Simply add this snippet into functions.php code.
function feed_author() {
if( is_feed() ) {
global $post;
$author = get_the_terms($post->ID,'authors');
$num_of_items = count($author);
$num_count = 0;
if ( $author ) {
foreach($author as $aut) {
$name .= $aut->name;
$num_count++;
if ($num_count < $num_of_items) {
$name .= ", ";
}
}
}
return $name;
}
}
add_filter( 'the_author', 'feed_author' );