Fairy Prion (source: Wikipedia)
Fairy Prions, Pachyptila turtur (Procellariiformes: Procellariidae), are pelagic birds found throughout the Southern Hemisphere, with large breeding colonies in Australia, New Zealand, the Crozet Islands, the Falkland Islands, and South Georgia.
The word “fairy” entered English around 1066 from the Old/Middle French feerie meaning “witchcraft” — I’m guessing Fairy Prions are thus named because they are the smallest of the six prion species, and fairies are generally thought to be small.
The word “prion” comes from the Greek πριόνι (“prioni“) which means “saw” (as in the thing you cut wood with) — prion bills are serrated, like saw blades.
Prions are a type of “petrels” which are named after St. “Peter,” who walked on water with Jesus in Mt. 14:22-34. When petrels forage, they often hover with their feet just barely not touching the sea, giving the appearance of, well, walking on water.
Pachyptila, the genus, comes from παχύς (“pachus”), meaning “thick” or “broad” or “stout” — Google translate suggests “plump” — and πτίλων (“ptilon”), meaning “feathers.” The word παχύς (“pachus”) comes up in English words such as “pachyderm” (literally “thick skin,” cf. dermatitis, dermatology, etc) and τίλων (“ptilon”) in “helicopter” (“spiral feather,” cf helix) and “pterodactyl” (“feathered fingers,” cf dactylic hexameter [versus iambic pentameter, which counts “feet” rather than “hands”], and also, remarkably, cf “date,” the fruit, which comes from the Latin dactylus > Greek δάκτυλος, because dates on date trees are shaped like fingers).
As for turtur, your guess is as good as mine, though it is the Old/Middle English word for “turtle.”