Fashion designer Stella McCartney has named her baby son Miller Alasdhair James Willis, it has been reported.
The daughter of ex-Beatle Sir Paul gave birth to 8lb Miller at London's exclusive Portland hospital last Friday.
It is not known where the name Miller has originated, but Stella turned to the McCartney family for her son's third name.
The 33-year-old has a grandfather called James Paul McCartney and brother named James Louis McCartney.
Alasdhair is the name of her husband, former magazine publisher Alasdhair Willis.
The couple married on the Isle of Bute, Scotland, in August 2003.
The couple have refused to comment on their child's name.