The process for changing your name + gender in germany is even more complex than in the UK.

You have to send an application to the court responsible for it (in your case, that's the Amtsgericht Schöneberg), then you pay 1500–2500€, then you have to get two psychological evaluations by psychologists on the courts list (Schöneberg might have provisions for you to name your own?), then you have a court date where the judge then decides whether they believe you'll stay trans forever (again, possibly Schöneberg gas provisions for citizens living outside of Germany).

Are you dual-national or only German? Because they might accept your Gender if you have a GRC, but you'd probably have to ask the court or your Standesamt.