This is a representation of a ‘typical’ company. Notice the flow, but also note what are defined as support functions. Most companies align to this basic representation to a large degree. Even service companies when you come to think about it. The most common problem in service implementations is to associate these functions with a company’s actual functional departments. One service client had a position titled Process Improvement Manager. That position was responsible for ‘quality’ related functions in the organization. Initially, one might have heard the title and equated it with a ‘production manager’ or similar.
My point here is to make sure you look closely and ensure your functional areas are well defined and the related responsibilities are clear. At that point you can start to align your functional representatives (management) with requirements.
ISO 9001 does not proscribe any particular functional division. It only requires that you define what each functional division is responsible for. You may not find a direct equivalence in your company with each function in the above. For example, if you are a service company you may (or may not) have equipment to calibrate. If you do repair work, you may not immediately notice it, but material stocking will probably be applicable.
Again, common sense has to come into play as you consider function responsibilities.