This chat can be used to provide support to your customers and answer their queries. In this scenario, the site visitors should not be able to talk to other visitors, instead they would only see support staff. To configure chat for this scenario, go to the settings/configuration page and set 'Show only admins in chat list' option to 'Yes':
In DrupalChat module, all users having administer_drupalchat permission are considered as support staff.
In WordPress iFlyChat Plugin, all admins of WordPress website are considered as support staff.