Hi,
At the first run on Messages the Preferences > Accounts in the app shows two accounts that you cannot delete (or Add anywhere else).
The iMessages is waiting for your Apple ID and the Bonjour one in normally set to be inactive (you need to tick the Box to "Enable this Account".
Bonjour is a zero set up account that will find other iChat/Messages accounts of other Macs on your LAN
If the iMessages account is Missing you will need to reinstall the OS as there is no way to install just Messages.
iMessages (an account within the Messages app) is not part of iCloud (it just uses an Apple ID that has to be iCloud valid).
In System Preferences > iCloud there is not set up for Messages, FaceTime, iTunes, Game Center, App Store, iBooks despite the fact you might use the same ID on all of them.
In System Preferences An Apple ID ending in @mac.com @me.com if linked to iCloud or @iclould.com can be used as a Valid AIM Screen Name due to an Agreement Apple has had with AIM for 15 years (since iChat (1) first came out).

8:13 pm Sunday; August 21, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)