You'd expect "no one" to have become one word, like someone, anyone, everyone. Presumably the reason it hasn't is because of the awkward "oo" that would create and perhaps also the similarity to "noon". That would indicate hyphenation as the logical compromise spelling, but hyphenation is broadly out of fashion for nouns, except a few neologisms, so two words it is. Mostly. Like "co-operative" and "cooperative" (does that mean "pertaining or relating to coopers"?), there ought to be scope for both.