How to display parent category label in Woocommerce?

Question

WordPress

Good time!
Faced with the task - you need to display the label of the topmost parent category, while I am in the product, or in another subcategory.
That is, if I am in the category Animals -> Large Animals -> Mammoths, then I need to search for and display the tag (animals).

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There is a theme function in php that displays the name of the genus category, but I can not figure out the output of the tag.
I will be grateful for any help.

The function of deriving the name of the genus category

function wc_origin_trail_ancestor($link = false, $trail = false) {
  if (is_product_category()) {
    global $wp_query;
    $q_obj = $wp_query - > get_queried_object();
    $cat_id = $q_obj - > term_id;
    $descendant = get_term_by("id", $cat_id, "product_cat");
    $descendant_id
      = $descendant - > term_id;
    $ancestors = get_ancestors($cat_id, 'product_cat');
    $ancestors = array_reverse($ancestors);
    $origin_ancestor = get_term_by("id", $ancestors[0], "product_cat");
    $origin_ancestor_id = $origin_ancestor - > term_id;
    $ac = count($ancestors);
  } else if (is_product()) {
    $descendant = get_the_terms($post - > ID, 'product_cat');
    $descendant = array_reverse($descendant);
    $descendant = $descendant[0];
    $descendant_id = $descendant - > term_id;
    $ancestors = array_reverse(get_ancestors($descendant_id,
      'product_cat'));
    $ac = count($ancestors);
  }
  $c = 1;
  if ($trail == false) {
    $origin_ancestor_term = get_term_by("id", $ancestors[0], "product_cat");
    $origin_ancestor_link = get_term_link($origin_ancestor_term - > slug, $origin_ancestor_term - > taxonomy);
    if ($link == true) echo '<a href="'.$origin_ancestor_link.
    '">';
    echo $origin_ancestor_term - > name;
    if ($link == true) echo '</a>';
  } else {
    foreach($ancestors as $ancestor) {
      $ancestor_term = get_term_by("id", $ancestor, "product_cat");
      $ancestor_link =
        get_term_link($ancestor_term - > slug, $ancestor_term - > taxonomy);
      if ($c++ == 1) echo '» ';
      else if ($c++ != 1 || $c++ != $ac) echo ' » ';
      if ($link == true) echo '<a href="'.$ancestor_link.
      '">';
      echo $ancestor_term - > name;
      if ($link == true) echo '</a>';
    }
    $descendant_term = get_term_by("id", $descendant_id, "product_cat");
    $descendant_link = get_term_link($descendant_term - > slug, $descendant_term - > taxonomy);
    echo ' » ';
    if ($link == true) echo '
    <a href="'. $descendant_link .'">'; echo $descendant->name; if($link == true) echo '</a>'; } }