thanks for reaching out to the wefugees community!
In order to change your name officially you need to go to your Bürgerbüro and file an Antrag (application) to change the name (this is possible in some cases if you have valid reasons other than „I just don’t like my name“). However this is only possible after you have gone through the process of Einbürgerung (naturalization).
Since you said you don’t want to change your last name I would advise you to use the preferred name in spoken contexts and to use both names in written official ones.
I hope my answer was helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.