Neverland. (Peter Pan's island) or perhaps Nim's Island? (Part of a movie.)
Or the island on which Alex was trapped with the Black Stallion in the book, The Black Stallion? Or Gulliver's Island, but I've never read or seen that :)
Sunshine Island
Jefferson Secondary, Clement Secondary, Harris Secondary, Frosterhill College,
Costa Bella
your mom's name
Hawaii green sox
A name that stands out, get up some name listings online if you must, and choose the least common name, commonly whatever names seem to fit the character's personality will do fine.
Some may, some may not. Depends on what they are reporting or their history was. They use fake names either to keep their real name private or legal reason. Or maybe just for fun.
kwakwaka'wakw
ohea
hungry for willys
Some examples of fake government names could be "The Ministry of Silly Walks" (from the comedy sketch by Monty Python), "The Department of Utter Nonsense", or "The Bureau of Imaginary Affairs". These are fictional names often used for comedic or satirical purposes.
Candy island Family island Shopping Mall island Fruit island Rainbow island Sports island Mystery island Holiday island Season island (Winter, spring, fall, summer) Nature island/Flower island Technology island Fred Meyer island Underwater island Etc...