Display the chosen shipping method label (and other related data, if needed) in cart page (or in checkout page)

gistfile1.txt

    foreach (WC()->session->get('shipping_for_package_0')['rates'] as $method_id => $rate) {

        if (WC()->session->get('chosen_shipping_methods')[0] == $method_id) {
            $rate_label = $rate->label; // The shipping method label name
            $rate_cost_excl_tax = floatval($rate->cost); // The cost excluding tax
            // The taxes cost
            $rate_taxes = 0;
            foreach ($rate->taxes as $rate_tax)
                $rate_taxes += floatval($rate_tax);
            // The cost including tax
            $rate_cost_incl_tax = $rate_cost_excl_tax + $rate_taxes;

            echo '<p class="shipping-total">
            <strong class="label">' . $rate_label . ': </strong>
            <span class="totals">' . WC()->cart->get_cart_shipping_total() . '</span>
        </p>';
            break;
        }
    }