Yesterday, we told how Rachel had given birth to their second son on Sunday and described him as "beautiful and healthy" in a tweet.
In a new post on her website thezoereport.com, Rachel has now confirmed her baby's name and uploaded a gorgeous black and white picture of herself, Rodger and their new arrival.
Alongside it, 42-year-old Rachel wrote: "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!"
Rachel, who also has a son called Skyler, kept quiet about her most recent pregnancy, before finally confirming that she was expecting her second child in September.
At the time, she said: "Rodger, Skyler and I hope that everyone had an amazing summer!
"Before we head into the chaos of fashion season, we wanted to take a moment to OFFICIALLY confirm that we are expecting another child."
It's been a year packed with celebrity births - see who else has had a baby in 2013:
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