With @mac.com and MobileMe issued @me.com name you can also sign in here as can AIM names.
Once you have signed it you get returned to this screen the top line welcomes you listing your Screen Name (Or Display name)
In Manage Account you can set the Display Name.
I have mine set to iChat Guru and when people don't have me in their Address Book and iChat this is what they see:-
This might be what is going on if a shared computer was logged in with one Screen Name that did not identify someone strongly enough.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously