'Pink cockatoo' was its official name (with Major Mitchell as an alternative) in the 1926 official RAOU checklist, and was reinstated as the official name in 2023 following the IOC's taxonomic change. Prior to 2023, 'Major Mitchell's cockatoo' was designated the official name for this species by the International Ornithologists' Union (IOC). Due to this, the former genus Lophochroa may be better considered a monotypic subgenus of Cacatua. In 2023, this species was reclassified into the genus Cacatua by the International Ornithological Congress although it represents a very basal member of the clade, it shares close morphological, behavioral, and vocal features to other members of the genus. Another indication of the early divergence of this species from the 'white' cockatoo lineage is the presence of features found otherwise only in corellas, such as its plaintive yodeling cry, as well as others which are unique to pink and the true white cockatoos, for example the large crest and rounded wing shape. Indeed, disregarding the crest, the pink cockatoo looks almost like a near- leucistic version of that species. Like the galah, this species has not lost the ability to deposit diluted pigment dyes in its body plumage, although it does not produce melanin coloration anymore, resulting in a lighter bird overall compared to the galah. The pink cockatoo is more closely related to Cacatua than is the galah, and that its lineage diverged around the time of or shortly after the acquisition of the long crest probably the former as this crest type is not found in all Cacatua cockatoos, so must have been present in an early or incipient stage at the time of the divergence of the pink cockatoo's ancestors. Citing Lear, William Swainson gave it the name Plyctolophus erythropterus.

Edward Lear painted it in his 1832 work Illustrations of the Family of Psittacidae, or Parrots. The scientific name commemorates the London naturalist and taxidermist Benjamin Leadbeater, who had given Vigors what would become the type specimen.

Irish naturalist Nicholas Aylward Vigors described the species in 1831 as Plyctolophus leadbeateri. The pink cockatoo ( Cacatua leadbeateri), also known as Major Mitchell's cockatoo or Leadbeater's cockatoo, is a medium-sized cockatoo that inhabits arid and semi-arid inland areas of Australia, though it is seen regularly in other climates, for example, South-East Queensland's subtropical region. Plyctolophus erythropterus Swainson, 1837

Cockatoo bird life span