Thank you for sharing your situation with the Wefugee Community!
I am not sure, if I fully understood your situation. What do you mean with "marrying on German documents"? It will be difficult to marry in Germany as long as you are in the asylum process. The authorities will most probably will not give you the permission to leave the country or to travel.
In case you want to marry in Greece, you may want to check the following thread, as similar questions were raised on this platform before: https://www.wefugees.de/803055/can-get-married-in-greece-although-asylum-case-is-incomplete?show=803055#q803055.
I hope this helps and please get back to us if any clarification is needed.
All the best,