What is the story behind the name changes of incoming popes? I am unfamiliar with the history and reasoning behind this.
The first pope to change his name was John II in 533. Believe it or not, his name at birth was Mercury! He couldn't very well keep the name of a pagan Roman god, (though we protest-ants are thinking "why not?") so he changed his name. There was actually a pope who was born Peter who changed his name to Sergius for obvious reasons.
So the answer to your question is, the pope changes his name for the same reason Robert Zimmerman changed his to Bob Dylan - for the business.