'No one' is the correct spelling.
You might think because 'no body,' 'some body,' and 'some one' have been changed to 'nobody,' 'somebody,' and 'someone,' 'no one' has also become 'noone'. But 'no one' does not obey this rule. It is probably because 'noone' looks unnatural and wrong.

'No-one' with a hyphen, is also commonly used as an alternative spelling to 'no one,' except for American English in which the hyphenated 'no-one' is not considered a correct spelling.

Consider these sentences:

Never write 'Noone'. It is a spelling error.