Setup Mode Problem

When I reassign an instrument (here: Klarinette 1 and 2), I get english instrument names - while the setup is set to german instrument names…

Indeed. If the player was already a Clarinet (with the English name) then when you reassign it will still be a Clarinet (with the English name). Select the instrument, click the disclosure arrow to the right, then Edit Names… Then click the Reset to Default button at the bottom and hit OK.