Claudia Schiffer names baby daughter Cosima Violet

The 39-year-old Schiffer had kept her new baby’s name a secret since her birth on May 14 until the entire family had been introduced, the model’s spokesperson told German daily Die Welt.

“Mother and child are both doing very well,” Schiffer’s spokesperson said.

The baby was born by Caesarean section at Portland Hospital in London, where the family lives. Other celebrity mothers have also delivered their babies at the central London hospital, including actress Gwyneth Paltrow and Lilly Becker, wife of former tennis champion Boris Becker.

Schiffer and Cosima and are now home resting, the spokesperson said.

Schiffer has been married to British film producer Matthew Vaughn since 2002. The couple already had two children, 7-year-old Caspar and 5-year-old Clementine.

Before the birth the supermodel gave an interview to Die Welt from her home in Notting Hill, London.

“I’m a lot more confident now, and that’s also because of my children and my husband,” Schiffer said.

The German edition of fashion magazine Vogue has devoted its entire June edition to Schiffer – adorning the cover with a naked portrait just weeks before gave birth.

Click here for the full Vogue cover featuring Claudia.

Taken by Schiffer’s long-time confidant and booster, German fashion designer Karl Lagerfeld, the cover shot follows in a long tradition of heavily pregnant celebrity photos started by Demi Moore in 1991.