welcome to our community!
First of all, you have to be patient. German bureaucracy usually takes some time to get its work done. Since you just handed in the documents a few days ago, it is totally normal that you have not received an answer yet.
If the Standesamt did not tell you to do anything else besides bringing your documents to the Ausländerbehörde, then you just have to wait. The Ausländerbehörde will refer back to you as soon as there is news concerning your case. Beyond that, I can only speculate since I don't know what exactly the Ausländerbehörde needs to check/change.
As far as I can see everything should be fine. Or am I missing the point here? Feel free to ask further questions if anything remained unclear or if I misunderstood the question.