The rule for creating a department
A department should exist when a different group of people answers that kind of request. Not when the request is merely different. If the same two people answer billing and technical queries, you have one department and two categories.
Signs you have too many
Tickets are constantly transferred between two departments. Several departments have one member. Customers pick the wrong one more than a fifth of the time. Each of these means merging, not more training.
Signs you have too few
One queue holds most of the volume and the people working it have visibly different skills. Urgent work waits behind routine work. Reporting cannot answer “how much of our effort goes to billing?”
Split by category before splitting by department
Categories are cheap to change and reversible. Departments involve people, addresses, targets and habits. Introduce the category, watch the volume for a month, and only then decide whether it deserves its own team.
Growing past twenty staff
At this size, add a layer rather than more departments: groups within departments for shifts and specialisms, and skills-based routing so tickets reach the right person inside the right team.