Remove ALL shipping method labels in WooCommerce Cart and Checkout

Paste the following code in functions.php:

/**
 * @snippet       Removes shipping method labels @ WooCommerce Cart / Checkout
 * @how-to        Get CustomizeWoo.com FREE
 * @sourcecode    https://businessbloomer.com/?p=484
 * @author        Rodolfo Melogli
 * @testedwith    WooCommerce 3.5.6
 * @donate $9     https://businessbloomer.com/bloomer-armada/
 */
 
add_filter( 'woocommerce_cart_shipping_method_full_label', 'bbloomer_remove_shipping_label', 10, 2 );
  
function bbloomer_remove_shipping_label( $label, $method ) {
$new_label = preg_replace( '/^.+:/', '', $label );
return $new_label;
}

Source: https://businessbloomer.com/woocommerce-remove-shipping-labels-cart-checkout-page-e-g-flat-rate/