Why would a German spelling of an English word be different from the spelling in English?
Sound designer is the grammatically correct spelling. Sound design also.
Capitalization of the words (when not starting a sentence) is used only as a part of e.g. a professional designation e.g. "John Smith, Sound Designer" or e.g. in marketing and company/product naming/branding e.g. "John's Sound Design Services" or in other cases where "sound design" is part of a name/title, i.e. it forms or is part of a proper name. E.g. the name of this forum can be written as "Sound Design" and not "Sound design", because in this case the word refers to the name of this forum (and in turn to this particular forum) and is a proper name.
But for example: "Today, I will practice Sound Design." is wrong and should be "Today, I will practice sound design.". Or "I heard about this Sound Designer that I thought I'd hire for my next movie." is wrong and should be "I heard about this sound designer that I thought I'd hire for my next movie.". Or "John is a Sound Designer." is wrong and should be "John is a sound designer.".