Are you saying that you can access your map service with the machine name but when you change that to an IP address it does not work? Please provide the URL that works, the one that does not work, and the error message you get.
Please clarify what behavior you desire with regards to the login. Do you want a system which requires no logins? Do you want to have a particular map service which does not require a login? Do you wish to disable access to a map service?