Gareth, If you are in Object Designer in Incident Management / Incident you will see a load of attributes at the bottom which are greyed out with hardly anything you can edit on them. If you look at Change Management / Change and Problem Mgt / Problem you will see the same attributes at the bottom.
Thats because those grayed out fields are inherited from Process Management / Process. Which is where you can go and amend them. Just remember if you amend, you amend for all the items which inherit from process, so thats call, request, change, problem, incident and the tasks for each as well