Rachel Zoe has named her baby son Kaius Jagger Berman.

The stylist and her husband Roger Berman announced the arrival of their second child on Twitter on Sunday, before sharing the tiny tot's moniker on her website yesterday. "As loyal readers of The Zoe Report, I wanted you to be the first to see a picture of the beautiful new addition to our family, Kaius Jagger Berman, aka 'Kai,'" she wrote.

The couple, who married in 1996, already have two-year-old son Skyler, who Rachel previously admitted was struggling to adjust to the idea of having a sibling. However, she insists her new family are doing well and are going to be staying away from the public eye over the Christmas holidays.

"Rodger, Skyler and I are madly in love and will be happily hibernating for the next couple of weeks. Thank you for all of your kind words, as they mean so much to us. Wishing you and your family a wonderful holiday and happy New Year!" she added.

Rumors that The Rachel Zoe Project star was pregnant began circulating in June, with the outspoken fashionista confirming the claims in a blog post this September. "We are beyond excited for Skyler to have a sibling and for us to fall in love all over again. We feel incredibly blessed," she enthused.