Have just tweaked your code to achieve what you need. See, if this works for you –
$taxonomyName = "age";
$parent_terms = get_terms($taxonomyName, array('parent' => 0, 'orderby' => 'slug', 'hide_empty' => false));
echo '<ul>';
foreach ($parent_terms as $pterm) {
$terms = get_terms($taxonomyName, array('parent' => $pterm->term_id, 'orderby' => 'slug', 'hide_empty' => false));
foreach ($terms as $term) {
echo '<li>'.$pterm->name.', <a href="' . get_term_link( $term->name, $taxonomyName ) . '">' . $term->name . '</a></li>';
}
}
echo '</ul>';
Specifically, I have added $pterm->name
within the <li>
tag which should give you parent term name along with each of its child term.
Please note: I have not tested it.