There are at least five artists that have used this name:
1. A rock band from the United States.
2. An alternative rock band from Portugal.
3. A singer from Japan.
4. A hip hop group from Serbia.
5. A progressive folk group from The Netherlands.
6. An epic heavy metal/space rock band from the UK. 1. Full Moon is a band featuring Neil Larsen and Howard 'Buzz' Feiten from the Larsen-Feiten Band

Read more about Full Moon on Last.fm.