Yes, they can but by default, your web portal only allows you to select which department the ticket can be assigned to. There are actually several settings you can change to allow more freedom for your users when submitting tickets.
Here are some of them
Status of the ticket (off by default)
- Open
- Solved
- Closed
Priority of ticket (off by default)
- Low
- Normal
- High
- Urgent
Department of the ticket (on by default)
- Your current departments
The agent of the ticket (off by accident)
- Any agents in your organization based on department
It is recommended that you leave the settings as such, but you may turn off and on whatever you like