How do I allow only registered users access to the helpdesk?

You are able to lock down your helpdesk to registered users only by going to Admin Settings > Security Configuration.

From this page, you can turn OFF the setting to "allow unregistered users to create ticket". This setting is recommended only for internal-facing helpdesks, and requires maintenance from helpdesk admin. Only those that have been previously set up in your helpdesk are able to submit tickets. Any new employees joining your company will have to be registered as a user in your helpdesk.

 
See other articles in User Roles