if i'm understanding your question correctly, then some people would say that it would be called anarchist. other people would say it would be communist (not in the soviet union/china sense of communist, but in what marx originally talked about as communism).
but i would argue that in a significant way, anarchy means a lack of something, more than it means a presence of something. for example, it means a lack of institutionalized hierarchy (some would say, any hierarchy). etc.
if you're asking what would the system of how people live their lives when there are not rules over them telling them how to behave, i don't think there's a name for it. if there were a name, it's quite likely that rules would be set up to protect that name.
but maybe i'm not understanding the question?