This is a very large software category as it may also encroach into call center management as well be cognizant of that when starting to look.
The software category you should consider is Helpdesk/Service Desk Management. a few categories are Manage Engine HSP, Team Support, Remedy, IssueTrak, Vivantio. Some software in this space also include project management and resourcing as well.
Hi, I advice you to use Comindware for IT Help Desk. From my own experience there is a big problem today when support team works bad. Sometimes it happens because of people and sometimes because of inappropriate software used by the team. The first factor must be used by the management team and the second one by the CTO. The software I am talking about is flexible. easy to use, provide real time report creation and PM functions.