If you have the money to buy a small island, would you? How will you enjoy it?

So Prince William and Kate Middleton honeymooned in a beautiful island. During the recession, some small Greek islands were said to be made available for foreign buyers. Nicholas Cage bought one ( not in Greece ) but as to whether he still owns it in light of his financial woes, who knows? But would you get one yourself if you have the means? What would you do with it? What name would you give it? ( added this question after reading @incendiarydan’s post )