Please refer to this article for the latest update.
How can I ensure the privacy of unauthenticated customers who use the Zendesk messaging Web Widget on a shared browser in the Agent Workspace? What happens when customers use a shared browser?
When customers use a shared browser the system attributes the same email to two separate users. For example, if user A starts a conversation using email A and name A, Zendesk creates a ticket with user A as requester A.
If user B starts a chat on the same browser with email B and name B, Zendesk creates a new ticket and attributes it back to user A due to the persistent nature of messaging.
To prevent this, customers with a shared browser setup should use the incognito mode on their browsers when initiating a message on the Web Widget. Visitors can also clear their cookies after they are done with each conversation.
If you are currently on messaging and have a setup where it is common for users to share a browser, you can set the Web Widget to Forget history. This setting ensures that the conversation starts fresh every time a customer initiates a conversation and previous conversations will not persist across the Web Widget and messaging channels.
For more information, see the article: About messaging.