Here is what I have and it works great for 1 shipping class, but want to have separate messages for different shipping classes:
// Display a custom text under cart item name in cart page
add_filter( 'woocommerce_cart_item_name', 'custom_text_cart_item_name', 10, 3 );
function custom_text_cart_item_name( $item_name, $cart_item, $cart_item_key ) {
// Here below define your shipping class slug
$shipping_class = '5-gallon';
if( is_cart() && $cart_item['data']->get_shipping_class() === $shipping_class ) {
$item_name .= '<br /><div class="item-shipping-class">' . __("Please call confirm shipping rates", "woocommerce") . '</div>';
}
return $item_name; }