You can assign each of your agents to different websites. In that way they can chat only with visitors from websites your agents are assigned to.
You can assign an agent to websites by following the steps below:
1. Click on Agents from the left menu and then click on Edit icon of the agent.
2. In the text field Handle chats from the following websites (separate with comma) specify the websites which this agent will be assigned to and click Save (leave that field empty if you want the agent to be assigned to all of your websites).
3. You're done!
Now your agents can chat only with visitors from the websites they're assigned to.