If memory serves me right.
I believe the original name was to be "Miami Sharks" until it was decided the Dolphins was the smartest of all aquatic animals, thus....Miami Dolphins.
"A contest was held in 1965 to choose the name of the new Miami AFL franchise. A total of 19,843 entries were submitted with over a thousand different names. A dozen finalists were screened by a seven-member committee made up of the local media. Names considered included the Mariners, Marauders, Mustangs, Missiles, Moons, Sharks, and Suns. The winning name, "Dolphins," was submitted by 622 entrants."