Finally, I am able to give an update on this. Have been travelling a lot, so it took a while...

When arriving at the rental car facility, I tried to set this issue straight, but nobody of the staff could tell me for sure how this would work.

They were all just guessing that there is a processing fee of a couple of bucks (like 20, the rep said) - and they will hand out the address of the renter.
But they denied that they could put a remark into my rental data or something compareable. "Just wait and see", they said.

So, I guess I will have to wait for a letter to arrive in Germany...

Thanks for all your help!