There isn't a limit to the numbe of anonymou users and there isn't a way to change that in the UI. You can turn off public sign up and only allow users that are on the customer list which would only allow the users that you send invitaitons to access Service Desk, however, they will count towards the license.
Additionally, if there are domains you would like to block you can restrict access based on the URL or IP in Tomcat, Nginx, etc:
Hopefully that can give you some ideas to get started!
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