Carla Bruni-Sarkozy. (Sean Gallup/Getty Images)

The Bruni-Sarkozy baby has a name: Giulia. France’s first lady Carla Bruni-Sarkozy, 43, announced it on her Web site Thursday, about a day after giving birth in a Paris hospital. President Nicolas Sarkozy, 56, meanwhile, carried on with business between trips to the clinic, accepting an oak sapling in honor of his new daughter during an official visit to a waste-management plant, reports AP. Don’t hold your breath for a first look at the baby: The supermodel/singer/global fashion icon said last month they don’t plan to release photos.