Disable visitor information
On your Setup page, there is an option to "Hide Visitor Information"
Enabling this option will remove some of the information you see when a visitor initiates a chat. The information removed is shown with an arrow below:
Using this option will also prevent the chatbox notifying you when a customer changes pages.
Please note that this only prevents the information showing within the chat. It is still available in the information panel, transcripts and reports.