When the DHL Versenden / Shipping module has been configured correctly, no additional shipping method for DHL is visible the checkout. This is normal.

The DHL module does not provide a new shipping method in the checkout. Instead, it uses the existing ones in Magento. You need to link the desired shipping methods with DHL via the box "Shipping methods for DHL Versenden / Shipping" in the configuration. If one of those shipping methods is selected in the checkout, the activated DHL services will be displayed, and the shipment can later be transmitted to DHL.

The shipping costs need to be configured directly in those shipping methods.