The most famous prison island in America is named after seabirds, and the name was probably meant for a different island.
In 1775 the Spanish naval officer Juan Manuel de Ayala charted San Francisco Bay. On his chart, "La Isla de los Alcatraces" was the island now called Yerba Buena, between San Francisco and Oakland. The English captain Frederick Beechey later attached the name to the rock we call Alcatraz. The Treasure Island Museum dates that to 1826 and calls it a mistake.
Yerba Buena then went through several other names, including Goat Island. It got its Spanish name, meaning "good herb," back in 1931. The birds' name stayed on the rock.
Which birds Ayala meant is less certain than the usual translation suggests. "Island of the Pelicans" is the popular version. Wikipedia notes that many people take it to mean gannets instead. The Treasure Island Museum says Ayala saw both pelicans and cormorants.
There certainly were a lot of them. In 1827 the French captain Auguste Bernard Duhaut-Cilly found the island "covered with a countless number of these birds." A gunshot, he wrote, sent them up "in a great cloud and with a noise like a hurricane."
The Spanish bird word has a murky history of its own. Etymonline says alcatraz meant "pelican" in 16th-century Spanish and Portuguese, and later also "cormorant." Its source is uncertain. One proposal is Arabic al-ghattas, "sea eagle." Another is Portuguese alcatruz, the bucket on a water wheel, from Arabic al-qadus, a jar or machine for drawing water. If that is right, the pelican was named for its pouch, a bucket built into its beak.
The same word gave English albatross. Sailors borrowed alcatraz for larger seabirds, and the spelling drifted toward Latin albus, "white." Etymonline dates albatross to the 1670s. So the prison in the bay and the bird around the neck of Coleridge's Ancient Mariner carry the same name.
The later history is the part everyone knows. The US Army finished Fort Alcatraz by 1858. The federal penitentiary received its first 137 prisoners on August 11, 1934, and closed on March 21, 1963. By then, few people hearing the name thought of birds at all.