The Shakespeare in Love Oscar winner, 33, and her British-born Coldplay frontman husband, 29, already have a daughter, Apple, born May 14, 2004. Moses is the name of a song Martin wrote for his wife in 2003.
Following months of speculation that she was pregnant, in January Paltrow confirmed that she and Martin were expecting. After a Screen Actors Guild screening of Paltrow's movie Proof, Lou Diamond Philips, about to moderate a panel on the film, introduced Paltrow as "a pregnant woman" and then asked her, "How far along are you?"
When a member of the audience asked her how she got her hair so shiny, Paltrow replied, according to TV's The Insider: "It must be the prenatal vitamins ... I've been taking them for a few years."
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Paltrow said that her husband suggested the name soon after she discovered she was pregnant. "It conjured such a lovely picture for me – you know, apples are so sweet and they're wholesome and it's biblical – and I just thought it sounded so lovely and ... clean," Paltrow told Winfrey. "And I just thought, 'Perfect!'"
"We love unusual names in the family," Paltrow's mom, Blythe Danner, told PEOPLE in January.
As for being a mom, Paltrow told Winfrey that the overwhelming love she feels for her child is "a whole new dimension in emotion that I've never experienced. It's crazy."