McCartney, the daughter of Paul McCartney, and her husband, Alasdhair Willis (search), turned to her family name for their son's third name, People magazine said Tuesday.
The 33-year-old fashion designer has a grandfather named James Paul McCartney and a brother named James Louis McCartney. However, it wasn't clear where the name Miller originated. A representative for McCartney wouldn't comment.
Willis, a former magazine publisher, and McCartney were married in August 2003. It is the couple's first child.
McCartney is recovering at an undisclosed London hospital, but her new line of clothing will be unveiled as scheduled in Paris on Thursday, the magazine said.
"Even though Stella can't be physically present to take a bow," McCartney's representative said, "the Stella McCartney show will proceed as scheduled."