Department is information managed in end user entity level.
Meaning that under Preferences -> end users -> every end user should have the department information entered.
So when an end user submits a SR SysAid will show the department information accordingly.
For an easy life you could import this information from AD/LDAP.
If the department information is not connected with an end user and end users can submit tickets from different departments, what you need to do is define a free custom field available in full edition a new list field in the translation change his name to department and use this field as free independent filed for entering this information.
I hope I have helped.
Let me know if there is anything else I can help you with.