function append_text_to_product_title($title, $id) {
    // Retrieve the text string to append
    $text_to_append = ' - New Arrival';

    // Append the text to the product title
    $title .= $text_to_append;

    return $title;
}
add_filter('woocommerce_product_title', 'append_text_to_product_title', 10, 2);

// Query the products
$products = new WP_Query(array(
    'post_type' => 'product',
    'posts_per_page' => -1
));
// Loop through the products
while ($products->have_posts()) {
    $products->the_post();

    // Get the current product ID
    $product_id = get_the_ID();

    // Get the current product title
    $product_title = get_the_title();

    // Append the text to the product title
    $new_product_title = $product_title . ' - New Arrival';

    // Update the product title
    wp_update_post(array(
        'ID' => $product_id,
        'post_title' => $new_product_title
    ));
}
// Reset the query
wp_reset_query();

function append_text_to_product_title($title, $product) {
    // Retrieve the text string to append
    $text_to_append = ' - New Arrival';

    // Append the text to the product title
    $title .= $text_to_append;

    return $title;
}
add_filter('woocommerce_product_get_title', 'append_text_to_product_title', 10, 2);

Метод 4. Прямое обновление базы данных

global $wpdb;
// Append the text to the product title in the database
$wpdb->query($wpdb->prepare("
    UPDATE {$wpdb->prefix}posts
    SET post_title = CONCAT(post_title, ' - New Arrival')
    WHERE post_type = 'product'
"));