You mention iMessages which is an Account option in Messages in Mountain Lion.
Although built on the iChat engine and with the iMessages account added to the features iChat can do it is not exactly the same.
An Account in Messages could be the iMessages account which as an Apple ID registered with iMessages server.
An AIM Account:- An AIM Name or Valid Alternative such as certain Apple Issued IDs ( ending email@example.com @me.com or @icloud.com)
A Jabber account ID:- these could include Googletalk and Facebook IDs
You can use Yahoo IDs in iChat 6 and Messages.
iChat and Messages will also list a Bonjour Account.
Lets presume that you only want to delete the name or ID from iChat or Messages.
Excluding the iMessages one in Messages and Bonjour in any version highlight the account in the App Name Menu in the Menu Bar > Preferences > Accounts
Now click the minus button ( - ) at the bottom of the list on the left hand side.
This will delete those accounts that have Buddy lists.
The Bonjour Account can only be turned Off by Unticking the "Enable this Account" Box.
In the iMessages Account use the Sign Out button.
In the case of Deleting them from the place they were registered that is a whole different ball game.
In the case of an Apple ID it cannot be deleted. (in Can in the event of Death be "Closed" by a relative on production of a Death Certificate).
You would have to investigate each place you have a registered name about there deletion process if they have one.
Basically the question is a bit vague.
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