Add parent product category names to the woocommerce_page_title() function (hook)

woocommerce-custom-category-name.php

<?php
add_filter( 'woocommerce_page_title', 'custom_woocommerce_page_title');
function custom_woocommerce_page_title( $page_title ) {
	$queried_object = get_queried_object();
	if ($queried_object->taxonomy == 'product_cat') {
		$tid = $queried_object->parent;
		while ($tid > 0) {
			if ($parent_obj = get_term($tid, 'product_cat')) {
				$tid = $parent_obj->parent;
				$page_title = $parent_obj->name . ' &gt; ' . $page_title;
			}
		}
	}
	return $page_title;
}