Endellion refers to the Cornish village of St Endellion, close to where they are holidaying and which Mr Cameron has visited over the years. (If you're an hotelier why not see our special offer on mattresses)
Downing Street said that the couple had received congratulatory messages from the Queen, the Prince of Wales, Gordon and Sarah Brown and French President Nicolas Sarkozy.
Mr Cameron spent the night at the Royal Cornwall Hospital in Truro where his new daughter was delivered by Caesarean section on Tuesday.
The couple's two elder children, six-year-old Nancy and four-year-old Arthur Elwen, have now visited their sister for the first time.
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