Changing name at Straßenverkehrsamt after it has been changed at the passport

[jsancs 0]

Hi guys,

I need some information on how to update the correct name at the Straßenverkehrsamt.

So I registered for a driving license and received the letter from TÜV Führerscheinbüro. Later my name got changed at my passport

and Bürgerservice already updated the Meldesystem.

 

The question is: do I have change the name at the Straßenverkehrsamt at this point or I have to complete the exams first and wait for

the license and then get it changed. If I can do it now, then whom do I need to contact, Straßenverkehrsamt or the TÜV Führerscheinbüro?