Я сделал некоторые исправления;добавьте этот код в ваши functions.php. Переменная $ post возвращает информацию о текущем сообщении (продукте):
//I didn't understand why you were using it, I believe it was wrong
//you should pass your function and not the woocommerce function again
//add_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_title', 5 );
add_action( 'woocommerce_single_product_summary', 'bwtom_show_attributes_title', 5 );
function bwtom_show_attributes_title()
{
global $product, $post;
$abv = $product->get_attribute ('pa_weingut');
$abb = $product->get_attribute ('pa_rebsorte');
$abn = $product->get_attribute ('pa_dac-lage');
$abm = $product->get_attribute ('pa_jahrgang');
echo "<h1 class='attribut_header1'>" . __($abv,'woocommerce') . "</h1>";
echo "<h1 class='attribut_header2'>" . __($abb,'woocommerce') . "</h1>";
echo "<h2 class='attribut_sub1'>" . __($abn,'woocommerce') . "</h2>";
echo "<h2 class='attribut_sub2'>" . __($abm,'woocommerce') . "</h2>";
//choose which one is most useful to you
echo $post->post_content;
echo '<br />';
echo $post->post_excerpt;
echo '<br />';
echo apply_filters( 'the_content', $post->post_content );
}