The anti-landmines campaigner made the revelation on CNN's LARRY KING SHOW in America and explained she didn't want to keep calling the baby "it".
She says, "It's our one little secret. We both know and we know the name and everything, but we ain't going to tell you."
And the blonde ex-model also laid to rest some of the furious speculation about a fracas Sir Paul was involved in last Friday (19SEP03) when he visited the DAVID BLAINE stunt in Central London.
The former beatle was said to have been part of an angry exchange with a photographer who tried to take his picture, and was also reportedly rude and abusive to members of the public.
Mills McCartney, 35, says, "They stood miles away and his press guy stupidly told the press that he was over there. And he (Sir Paul) saw the press coming towards him.
"So he ran off to the car and the paparazzi were chasing after him. The last thing he wanted on his night out was to have the press around.
"He just said, 'No I don't have anything to say', so the next day it was all 'punch up, drama'.
"His people tried to stop the paparazzi but Paul just got into his car and went."23/09/2003 19:50