You say "MacBook Air" as part of your Specs.
You also list iOS 6.0.2 which would tell me you have an iPhone or iPad
You have not said what iChat version you are using or which OS X version you have on the MacBook Air.
You can create AIM names at the AIM registration page.
These tend to be plain "Username" type names
You can also use Apple ID issued by Apple (@mac.com @me.com and @icloud.com) as valid AIM Names.
These tend to be entered under the AIM option in later version of iChat.
There can be issues with using iCloud Issued IDs in older versions of iChat pre and including iChat 5
The iCloud @me.com and @icloud.com are used in iChat 6 and Messages in Mountain Lion.
These two version do a dual login to AIM and to me.com
This login to me.com allows the AIM server to "read" the password.
Earlier version do not have this dual Login and the names will not work.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously