According to this Jamaican government website:
The origin of the name ‘Docor-bird’ is somewhat unsettled. It has been said that the name was given because the erect black crest and tails resemble the top hat and long tail coats doctors used to wear in the old days. Other schools of thought believe that it refers to the way the birds lance the flowers with their bills to extract nectar.
According to Frederic Cassidy the bird is an object of superstition. The Arawaks spread the belief that the bird had magical powers. They called it the ‘God bird’, believing it was the reincarnation of dead souls. This is manifested in a folk song which says: “Doctor Bud a cunny bud, hard bud fe dead”. (It is a clever bird which cannot be easily killed).