I was in a similar situation back in 2015 when i joined a network manager who had just taken over from a managed IT service.
People didn't trust IT staff one bit and felt that if they did bother to submit a ticket, it wouldn't get done anyway! I found the best thing to do is to just get on with the job for a while, then ask for feedback later.
Once people see what a great job you are doing, they'll be singing your praises anyway.
Fast forward to 2017 and i was in the same school, a new deputy head starts and he has an axe to grind - so we send out a survey, and since the reputation had improved so much, he didn't have a leg to stand on!
IT Support 1 - Deputy Head 0