Welcome to our community and thank you for your question!
After being accepted as a refugee you will receive a so-called blue passport. I'm not sure whether it will be sufficient to prove your identity at Standesamt.
Do you still have your home country's passport? Usually you have to hand it in at Standesamt in order to prove them that you really are the person that you claim to be.
The easiest way to find out whether the blue passport is sufficient or not might be, to just go to Standesamt and ask them about the options you have.