How are you proposing a moon be defined? From the Wikipedia article: "There have been large generic searches for small moons, actual proposals or claimed sightings of specific objects in orbit, and finally, analysis and searches for those proposed objects. All three of these have failed to confirm a permanent natural satellite."

Also from Wikipedia: "A natural satellite or moon is a celestial body that orbits a planet".

There have been no other confirmed moons of Earth besides 'The Moon'.