Huh (not a native speaker). This seemed obviously wrong to me: it is clearly a single negative pronoun syntactically, not the determiner no modifying the animate(!) pronoun one—for example, you can’t add adjuncts: *no great one, like *every great one, *any great one, or even just *a great one, sounds like it’s about Lovecraftian Great Ones or inanimate used cars instead of the faceless but animate pronominal “one”.
Then I looked it up, and it turns out that both “no one” and “no-one” are accepted spellings for this linguistic gadget while “noone” is rejected by prescriptivists as a confusing spelling because of the double “o”, even if it would be in line with “everyone” etc. “Noöne” is admittedly funky and nonstandard, but if the no-diaeresis concatenated version is rejected because it’s confusing (though come on English, your whole spelling is nuts, why are you so stubborn on this one), then the diaeresis version should be completely acceptable.
Then I looked it up, and it turns out that both “no one” and “no-one” are accepted spellings for this linguistic gadget while “noone” is rejected by prescriptivists as a confusing spelling because of the double “o”, even if it would be in line with “everyone” etc. “Noöne” is admittedly funky and nonstandard, but if the no-diaeresis concatenated version is rejected because it’s confusing (though come on English, your whole spelling is nuts, why are you so stubborn on this one), then the diaeresis version should be completely acceptable.