Often we want to add a custom message on a shipping method or rate. If you are handling multiple methods you can simply use the “woocommerce_after_shipping_rate” action on your functions.php file:
add_action( 'woocommerce_after_shipping_rate', 'action_after_shipping_rate', 20, 2 );
function action_after_shipping_rate ( $method, $index ) {
// Targeting checkout page only:
if( is_cart() ) return; // Exit on cart page
if( strcmp('Your Shipping method label', $method->label) == 0) {
echo 'Custom Message';
}
}