First of all, you need to have in mind that questionnaire you'll send to your customers need to have follow-up. That means - from the answers you'll receive there must be a clear conclusion and plan what to do with it (especially when the answer implies something that is not OK).
I would suggest to divide questions in two groups:
1. Communication related - that would give you the answer regarding communication capabilities of your staff. So, questions could be: Do Service Desk (SD) staff communicates in clear and unambiguous way? Are they calm and patient when talking to you? Are their explanations and/or reasoning understandable for you?
2. Competence related - here you'll get feedback about the quality of your SD staff work. So, here are few examples: Do you get your issues resolved while calling our SD? What is the quality of provided solutions? Are the issues resolved in timely manner (be careful while interpreting the answer - users need to be familiar with SLA)?
This article can help you further: "
Service Desk staff – a window to the IT organization" https://advisera.com/20000academy/blog/2014/02/18/service-desk-staff-window-organization/