Downing Street has revealed that the new-born daughter of Prime Minister David Cameron and his wife Samantha is to be called Florence Rose Endellion.
Endellion refers to the Cornish village of St Endellion, near where they have been holidaying and a place which Mr Cameron has often visited over the years.
The couple have received congratulatory messages from the Queen, the Prince of Wales, Gordon and Sarah Brown and French President Nicolas Sarkozy.
Their two elder children, six-year-old Nancy and four-year-old Arthur Elwen, have also visited their sister for the first time.
Samantha and baby Florence are expected to remain in hospital until the weekend.