When you go into the Initial Activity Notification Detail display, you will see there is just one rule listed, the Default Initial Notification Rule.
What is needed here is the creation of new Notification rules. You would navigate to the Notification Rules listings and choose to "Create New"
In the creation of the Notification Rule for each Department, you will need to fill in two things to make this work specific to the given Department: the Condition and the Message Template.
The condition is basically a Site Defined Condition Macro that would test if the given ticket belongs to the given department. Testing for this varies, from using a field in the ticket that references the Department, or if the affected end user's Department is the testing attribute.
The Message Template is a template you can create anew, and have its field contents copied from the Initial Activity Notification, including any elements unique for the given Department's notification.
After you have defined two sets of Notification Rules, one for each Department, which will in turn have you create a separate condition to test for the given department and a Message Template unique to each Department, you would then add the Rules into the Initial Activity Notification, ie:
Once everything is said and done, you would now have this listed:
Notice there are now three Notification Rules, the Default Rule and the two Department specific entries created.