Live Chat Display to Keep to Generic User (e.g. Sales or Support) Even When Assigned

Hi Team, (submitting on behalf of the customer), 

 

The customer would like that the Live Chat Display to Keep to Generic User (e.g. Sales or Support) Even When Assigned. Currently, when the chat is assigned to a user, it changes the name of the user, they would like the ability to keep to their original display name but internally in Conversations inbox, differentiated with different users. 

 

Otherwise, if they can setup a chat specific profile or alias that would be useful.