Instead of “chaos”, it sounds like that place was “free”.
Try–Freeman.
Being a huge fan of Get Smart, I’d go with Kaosson, or O’Kaos. How much more American can you get than Get Smart?
(emphasis mine) Pronounced “Old Sock”?
Ataxia - Literally a state of no control. But it’s commonly used as a medical term for a loss of musle control.
Bedlam - A English insane asylum. Later became a term for any wild place. Somebody already mentioned O’Bedlam.
Coventry - Robert Heinlein had a lawless place called Coventry in one of his stories.
Ginian - An Old English word for chaos. Could be adapted as MacGinian, McGinian, or O’Ginian.
Nihil - Literally means nothing. The root for nihilism, a political belief that rejects all political beliefs.
Tarakhe - A classical Greek word for chaos.
Upon further research, it appears ginian might be better translated as “yawn”. It became connected with chaos because early definitions of chaos refered to a gaping chasm or void.
Um, no, pronounced like OLODSOC.
Or, more specifically, /oʊladsak/.
Havoc, Rick Havoc.
Sorry, given the chance to change your real life name, you must be called: McLovin’
Just McLovin. It’s badass.
Hehehe, I thought about McLovin, but I don’t need to legally change my name for that, just get a fake ID!
I’m strongly leaning towards Kaos as a last name. O’Kaos would be more accurate but also less international.
What do you think is a first name that goes best with Kaos?
Something that starts with a hard K sound - alliteration is tuff.
Kuir Kaos?
Killroy Kaos.
Kronic Kaos.
Johnny Kaos.
Oklahoma Kaos.
Kermit! 
Armistice M. Kaos
Dredd Q. Kaos
Max Kaos?
Maximilian P. Kaos.
Kanye Kaos.
Actually, Kanye O’Kaos is pretty rad.
Ernst Stavo Kaos.
The Third.
George T. Horseprotection!
Maximillian Von Kaos