(WordPress) How to get custom taxonomy parent name?

Using two nested foreach you prevent n+1 db queries, where n is the number of child terms:

<?php
$_cats = array();
$args = array(
  'orderby' => 'id', 'order' => 'ASC', 'taxonomy' => 'album'
);             
$categories = get_categories($args);
if ( ! empty($categories) ) { foreach( $categories as $category ) {
    if ( $category->parent != 0 ) {
        if ( ! isset($_cats[$category->parent]) ) {
            $_cats[$category->parent] = array( 'terms' => array() );
        }
        $_cats[$category->parent]['terms'][] = $category;
    } else {
        if ( ! isset($_cats[$category->term_id]) ) $_cats[$category->term_id] = array();
        $_cats[$category->term_id]['parent_name'] = $category->name;
        $_cats[$category->term_id]['terms'] = array();
    }
} }
if ( ! empty($_cats) ) { foreach( $_cats as $parentid => $children ) {
  if ( ! empty($children['terms']) ) { foreach( $children['terms'] as $term ) {
    $album_url = site_url() . '/album/' . $term->category_nicename;
    $cover =  site_url() . '/covers/' . $term->category_nicename . '.jpg';
?>
<li class="span3">
<div class="thumbnail">
  <a href="https://wordpress.stackexchange.com/questions/108522/<?php echo $album_url; ?>" rel="nofollow">
    <img src="<?php echo $cover; ?>" alt="<?php echo $term->name; ?>">
  </a>
  <div class="caption">
  <a href="https://wordpress.stackexchange.com/questions/108522/<?php echo $album_url; ?>">
    <?php echo $children['parent_name'] . ' - ' . $term->name; ?>
  </a>
  </div>
</div>
</li>
<?php } } } } ?>

… and please, the right PHP open tag is <?php not <?.