How to assign where/who gets incoming chat messages from users before their case is assigned to anyo

When our users start TeamViewer and they initiate a chat message, how do I control who sees that incoming chat message? Right now, when a user starts TeamViewer and before we assign the case so a specific support person, and that user sends a chat, the message only goes to one support person. How do I set where that chat message is being sent?

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