I can't find a list of the cockatoo species. I've found the information of there being 20 different cockatoo's, but where can I find a list of names?

Try 21. The following list also shows subspecies:

1. Cockatiel, Nymphicus hollandicus
2. Palm Cockatoo, Probosciger aterrimus
3. Red-tailed Black Cockatoo, Calyptorhynchus banksii
4. Glossy Black Cockatoo, Calyptorhynchus lathami
5. Yellow-tailed Black Cockatoo, Calyptorhynchus funereus
6. Short-billed Black Cockatoo, Calyptorhynchus latirostris
7. Long-billed Black Cockatoo, Calyptorhynchus baudinii
8. Gang-gang Cockatoo, Callocephalon fimbriatum
9. Galah, Eolophus roseicapilla
10. Major Mitchell's (aka Leadbeater's) Cockatoo, Lophochroa leadbeateri
11. Yellow-crested (aka Lesser Sulphur-crested) Cockatoo, Cacatua sulphurea pets question and answers,www.5d2d.com
11a. Abbott's Cockatoo, Cacatua sulphurea abbotti
11b. Timor Cockatoo, Cacatua sulphurea parvula
11c. Citron-crested Cockatoo, Cacatua sulphurea citrinocristata
12. Sulphur-crested Cockatoo, Cacatua galerita
12a. Triton Cockatoo, Cacatua galerita triton
12b. Eleonora Cockatoo, Cacatua galerita eleonora
12c. Fitzroy Cockatoo, Cacatua galerita fitzroyi
12d. Greater Sulphur-crested Cockatoo, Cacatua galerita galerita
13. Blue-eyed Cockatoo, Cacatua ophthalmica
14. White (aka Umbrella) Cockatoo, Cacatua alba
15. Salmon-crested (aka Moluccan) Cockatoo, Cacatua moluccensis
16. Long-billed Corella, Cacatua tenuirostris
17. Western Corella, Cacatua pastinator
17a. Muir's Corella, Cacatua pastinator pastinator
17b. Butler's Corella, Cacatua pastinator butleri
18. Little Corella, Cacatua sanguinea
19. Tanimbar Corella (aka Goffin's Cockatoo), Cacatua goffiniana
20. Solomons Cockatoo, Cacatua ducorpsii
21. Red-vented Cockatoo, Cacatua haematuropygia

http://en.wikipedia.org/wiki/Cockatoo (which I don't feel bad about copying from, because I've contributed a fair amount to their parrot section).