Hi,
order_shipping_method only contains the folder name of the shipping plugin.
If you created shipping methods for the "HikaShop manual shipping methods plugin" then it's normal that you only see "manual" in there.
order_shippping_id contains the id of the shipping method.
The name of the shipping method is not stored in the order.
It is only available in the hikashop_shipping table, in the shipping_name column.
That information is not available in the listing of the orders.
What you can do in your mass action is to use an action "run mysql query" and use that query:
UPDATE #__hikashop_order SET verzendmethode = (SELECT shipping_name FROM #__hikashop_shipping WHERE shipping_id = {order_shipping_id}) WHERE order_id={order_id};
Note however that this won't work by ideal for dynamic shipping methods like UPS, USPS or FedEx as the name of the shipping method doesn't contain the shipping service (standard, express, international, etc). For these shipping methods, it would require some PHP code to be written to request the complete shipping method information to the shipping plugin. It would require some proper development.