Responders have the option to allow their assigned users to message them anonymously. This feature provides users with even more of a comfortable way to ask personal questions, report a situation, or share a concern they are having while protecting their identity.
On the Messages Screen on the mobile version of the app and on the Discover Screen for the online version of the app, their is a small icon of a person - this indicates whether or not you allow users who have access to you to send anonymous messages.
If you choose to turn this off, simply click on the icon and it will become dim.
This will disable the ability for assigned users to message you anonymously.