How to update WordPress order

I have made this function:

add_action(‘woocommerce_checkout_update_order_meta’, ‘my_own_function’);

function my_own_function ( $order_id ) {
$order = new WC_Order($order_id);
$order->shipping_last_name = ‘TEST’;
}

Now if I write the $order->shipping_last_name to a log-file in that function, then the name is correctly printed as TEST. But when I recieve the order, then that last name is the value that user gave when ordering.

So I am not sure if that function is called before the order is updated with the user given values, or is that order actually never saved with my updated value? How could I do this so that the value would be saved properly?