Assuming the artist’s name is the also the title for your “artist” post type, match it with the “artist_name” custom field in your “release” post type.
On your “artist” single post template:
// args
$args = array(
'numberposts'=> -1,
'post_type'=> 'release',
'meta_key' => 'artist_name',
'meta_value' => the_title()
);