Having given it a bit of thought I cannot come up with many animals whose names have entered the common speech as an adjective. Other than of course, Jumbo.
Jumbo was sort of a rock star in his day. According to his wikipedia page he was born in 1861 in present day Mali. He was sent to a zoo in Paris for a while then in 1865 transferred to the London Zoo where he was quite the favorite of the children. His name is likely a variant of the Swahili word jumbe, meaning chief.
The flamboyant showman P.T. Barnum purchased Jumbo in 1882. Barnum was never shy about publicity and Jumbo related advertising is fairly common, including this patent medicine trade card of the era.
Here is more from P.T. on the subject of elephants and liniment, from an 1886 Centaur Liniment almanac.
One wonders if the little elephant pictured was the one known as Tom Thumb. If so it would seem an ill omen. In 1885, according to the ever truthful and never known to fib Mr. Barnum, Jumbo was struck and killed by a locomotive while trying to save Tom Thumb from danger.
The marvelous website Roadsideamerica, to which I have linked before, has a nice account of what became of Jumbo post mortum, including this photo of the great elephant's ashes which reside in a peanut butter jar in the Athletic Director's office of Tuft's University. It is said that rubbing it brings good luck to their teams.
*although I understand that his bones are in the New York Museum of Natural History somewhere.