It will be different depending on if the select field on the post allows a single choice or multiple choices.
With a custom field you’re going to need to do a WP_Query for every name in the loop. http://codex.wordpress.org/Class_Reference/WP_Query
// select single
// all of this goes inside your foreach loop
$args = array(
'post_type' => 'post',
'posts_per_page' => 1, // only need 1, just checking for any posts with the value
'meta_query' => array(
array(
'key' => 'family_name'
'value' => $family
)
)
)
$query = new WP_Query($args);
if (count($query->posts)) {
echo '<li>' . $family . '</li>';
)
// multiple choices allowed
// all of this goes inside your foreach loop
$args = array(
'post_type' => 'post',
'posts_per_page' => 1, // only need 1, just checking for any posts with the value
'meta_query' => array(
array(
'key' => 'family_name'
'value' => '"'.$family.'"',
'compare => 'LIKE'
)
)
)
$query = new WP_Query($args);
if (count($query->posts)) {
echo '<li>' . $family . '</li>';
)
Either way, if there are a lot of choices then this is going to be extremely slow. You would be better off in the long run to use a custom taxonomy, something that’s built right into WP, then you just need to use get_terms() with the right arguments https://developer.wordpress.org/reference/functions/get_terms/
