Messages agent wants to use your confidential information stored in “” in your keychain
This fixed it for me (though note the caveat at the bottom)
Open /Applications/Utilities/Keychain Access.app, search for message, which in my case came up with two keys that I deleted. This required Administrator rights, though.
iCloud still wonky though
Probably because I trashed some of my preferences. I can live with that for the time being as it is not in my face every ten seconds.