I've always written it "noone". The spell checker always tells me it's wrong. So do the dictionaries.

More significantly, Fowler in Modern Engish Usage also agrees with splitting the word. However his reasoning is that spelling it as one word would result in a "natural tendency to pronounce noone" - and that seems very questionable reasoning indeed, because I doubt if anyone ever would actually do that (except when it's a surname); and the normal way to write "everyone", "someone" and "anyone" is as one word.

So I'll probably continue to use "noone", which has been used by many perfectly respectable writers. It just looks right, to me.

I imagine people called Noone must get get a bit irritated with being teased about it. But then "Nemo" is a very popular character these days.