No one is correct. Noone and no-one are both incorrect spellings.

If you're confused whether it's correct to write "noone" or "no one", you're in the right place! This is a commonly mistaken phrase.

Noone vs. No One

Noone is a misspelling of no one, which is a phrase meaning "no person". There should always be a space separating these words: "noone" isn't its own word. Since no one is not a hyphenated compound word, using a hyphen  to write "no-one" is also incorrect.

However, don't get this confused with "nobody", which is one word! "No body" and "no-body" are incorrect. Another potential confusion is with "anyone" or "anybody", which are both written as a single word.

The words any, every, some, and no can be merged with the word body to form one word.

Any + body = Anybody
Every + body = Everybody
Some + body = Somebody
No + body = Nobody
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However, when the any, every, some, and no are combined with one, only the first three will become one word while the last will result in two words (no one).

Anybody → Anyone
Everybody → Everyone
Somebody → Someone
Nobody → No one

Note that anyone, everyone, and someone call all be written as two words depending on the context, but no one would never be written as noone or no-one.

Google Books Ngram Viewer shows that no one is the clear winner out of no one, noone, and no-one. This is because no one is the only correct spelling.

Then is there a difference between no one and nobody? Although both have the same meaning, no one is typically seen as more formal than nobody. Both no one and nobody are used in spoken English, but no one is more commonly used in written English. If you take a look at the chart below, you can see that no one is more commonly used than nobody in Google’s corpus of published books.

The following are example sentences containing no one. Notice that you can replace no one with nobody in any of the sentences and;

  1. No one told me the venue changed.
  2. He told no one about his secret.
  3. No one knew where the file was saved.
  4. There’s no one who knows the password to this computer.
  5. No one listened to Marie when she was angrily ranting.
  6. No one can fix a computer better than he does.
  7. She had a skill no one else had.
  8. I realized no one knew I entered the room.
  9. No one was around to help the elderly woman.
  10. Greg assumed no one was against his plan.
  11. No one knows the secret recipe for Grandma's famous apple pie.
  12. The unique bond between siblings cannot be replaced; no one can do it.
  13. The sudden change in weather brought heavy snowfall, surprising everyone, but no one expected it.
  14. The office was unaware of the surprise birthday party being planned for the boss; no one had a clue.
  15. No one enjoys being left out during social gatherings is something no one enjoys.

The misspelling noone is always incorrect, but there are times when no—one can be used in a sentence when used with an em dash. However, it can only be used as two separate words in a context where it do not mean nobody.

He said no—one of the conditions was bothering him.
The manager responded with a no—one of his concerns was that there wouldn’t be enough food.

There are also other words that when combined with no, become one word. Such words include thing and where.

No + thing = Nothing
No + where = Nowhere
No + body = Nobody
No + one = No one

Notice that in the list above, only no one remains two words.

Although rare, there is a possibility that noone is a misspelling of the word noon, which is a completely different word than no one. Make sure you proofread your paper and use a grammar checker to catch any spelling errors.

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References:

Thesaurus results for NO ONE
Synonyms for NO ONE: nobody, none; Antonyms of NO ONE: everyone, anyone, someone, everybody, somebody, anybody