The 24-year-old singer, who made her first public appearance in months at 70th annual Golden Globe awards on Sunday, said the name of the baby is too personal, reported E! Online.
"I'm exhausted that's how it's changed me. I've got eczema from sterilising bottles so much in water. I'm not revealing his name. I'm not ready, it's too personal and intimate. I'm enjoying him on my own at the moment," she said.
At the ceremony in Los Angeles, 'Skyfall', the theme song for the latest James Bond movie, sung by Adele, was named best song.
Collecting her prize the singer had said, "I'd like to thank Paul Epworth who I did the song with. Daniel Craig you've been such a wonderful Bond.
"And this is for my husband Simon who convinced me to do it and to my lovely son. Thank you very much."
