The information in "Street line 2" or "addressAddition" (German: Adresszusatz) is correctly transmitted to DHL, which can be verified in the log. However, it is not visible on the PDF label.
DHL processes this information only for specific destination countries. Depending on the country, the information may not be visible on the label at all. For shipments to Austria, the information is shown, but not for shipments to Germany.
This behavior of the DHL Webservice (API) cannot be changed through the Magento extension!
To ensure that the extra information is visible on the label, the field "Company" can be used which is available in Magento by default. The field is mapped to "Name2" and will always be shown on the label. There is no validation for this field.
If necessary, the label at the checkout field "Company" can be modified to indicate that other information can be entered as well (e.g. apartment, floor, post number, etc.).