I just read this article recently that mentioned the name change:
Carnival will redo Destiny, stern to name - Travel Weekly
Could just be a PR
spin, but this is the reasoning quoted:
Mark Tamis, senior vice president of guest operations for Carnival Cruise Lines, explained: "When we started to look at the project and plan the layout and saw how much new there was going to be, including the renovation of cabins and corridors, it's going to be a completely new experience, and we knew we should rename the ship.
"It's a rebirth for the Destiny, and as we went through all the possible names, it came down to the fact that fun and sun are the DNA of Carnival Cruise Lines. So 'Sunshine' really resonated."
Tamis said Carnival was not concerned that Royal Caribbean International's two newbuilds are operating under the working name "Project Sunshine."
"Many names are shared throughout the cruise industry," he said. "We settled on the name Sunshine quite awhile ago. I don't foresee any confusion about it."