Shen-zin Su

Not tameable!

Background: the turtle that would be Shen-zin Su was just a normal sea turtle until he became friends with the Pandaren Liu Lang. Liu Lang hated the sedentary lifestyle of his fellow Pandaren and wanted to set out for adventure, but how would he ever find his way back to Pandaria through the mists? Liu Lang must have paid attention in biology, since he knew that sea turtles always have an instinct that guides them back to the exact same beach they were born, similar to how birds know where to migrate. He named his pet turtle Shen-zin Su after a kindly merchant who gave him a free umbrella named Shen-zin.
Over the years, Liu Lang would continue to travel from Pandaria into the outside world and back again on the back of his pet turtle. Shen-zin Su would continue growing, eventually to enormous size. This probably surprised everyone except those who played the classic Warcraft II strategy game where Horde-allied goblins rode giant sea turtles into battle like submarines. This turtle however grew large enough that a colony of like-minded Pandaren who wanted to see the world were able to settle on the back of Shen-zin Su and traveled all over the place. This turtle would eventually grow to the point where most onlookers would mistake it from an island wandering from place to place. Thus, the shell of Shen-zin Su would eventually be called "The Wandering Isle."
Shen would eventually stop returning to Pandaria, probably because of the death of his beloved master Liu Lang. Shen probably outlived his master (150 dude, and still young!), content to allow the Pandaren on his back to live in peace, happiness, and blissful ignorance of the outside world. Ironically, Liu Lang had created a place almost as sedentary and dull as the place he sought to escape.
However, this peace would come crashing down when an Alliance airship carrying Horde prisoners crashed into the side of the turtle by sheer chance. After a near-death experience for Shen, the Pandaren of the Wandering Isle, feeling the same want of adventure that Liu Lang felt so long ago, choose between Tushui and Huojin to join the Alliance or Horde.

Shen-zin Su is The Wandering Isle, because he is a gargantuan Sea Turtle, and when you think about why the [race=24] starting zone carries that name, it makes perfect sense!