The format of these longer system names is described in the section on the Internet (section 3.1).
If your login name on the remote machine is different from the one you use locally, you need to give your login name as part of the command, e.g.
% rlogin fog.cs.cascadia.edu -l fjoneswill log you in to the remote system with user name fjones. If you forget the -l option, you will still be able to log in. rlogin will first try to log you in with the wrong login name and prompt you for a password. Just type a return, and then you will see the usual prompt that asks you for both a login name and password and you can continue.