I actually take that back on the second bit of code. Since the field does not exist yet you must use the field key
add_action('acf/save_post', 'update_name_provider_field');
function update_name_provider_field($post_id) {
if (is_admin()) {
// don't run in admin
return;
}
if (get_post_type($post_id) != 'YOUR CUSTOM POST TYPE')) {
// don't run if not your post type
return;
}
// use the acf field key here
update_field('field_01234567', get_current_user_id(), $post_id);
}