Despite Sir Haldimar's enthusiasm about the name and the fact it was used in Jaynar, you must remember that BOTH of you are relative newcomers to the University. I think you may be right in dividing magic into more than three fields. Methinks that is too important a division to ignore. I include the enchantment of items in the definition of alchemy. Warlocks are evocation specialists and somewhat into conjuration.
Mystics are divination specialists and also dabble in summoning.
It might be worth figuring out how these students and faculty are split between the various departments. Look for the new version in the kristopan file area. Since he took the job then it follows that the name was changed. MIT Dream on fan-boy. Such is not the way the world works.