It is important to be able to ban someone annoying from the LiveChat if we consider him abusing of this function. It could be great to define a duration in his profile directly from the agent panel. In the front-end, the best thing is just to hide the LiveChat if he is banned, so the customer don't know he is banned but cannot chat during the ban period.
This is a great question, thank you. You are able to block a user from chatting, if you were to log on to our support site (support.deskpro.com), click on Guides > Agent Guide > Chat > Chatting with Users > Chat Details > Block User.
Or you follow the link I have provided below.
https://support.deskpro.com/en/guides/agent-guide/chat/chatting-with-users#chat-details
Please contact our Support Team if you have any further queries