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The couple celebrated the arrival of their second child around seven months ago and have remained very secretive about the tot's moniker.
Us Weekly magazine has claimed that the couple have gone with Elula, the Hebrew name for August.
Isla - who also has a three-year-old daughter Olive - recently joked that she calls her baby 'Taliban' in a bid to keep her out of the public eye.
So secretive
Speaking about why she is so secretive, the Rango actress told Elle magazine: "With the name, I keep making jokes like, 'It's called Taliban Perez Baron Cohen'.
"I just feel my children didn't choose a career in the limelight and unfortunately, I get followed.
"I'm not complaining about my job. I'm completely aware of how lucky I am. But until they decide on a job in the public eye, I want to protect their privacy."
Isla - who married Sacha in a secret ceremony last year after converting to Judaism - has also said she feels it's her responsibility to keep them out of the public eye.
She said: "Motherhood is my favourite topic but I never talk about it publicly. As much as I love what I am doing, and I am so fortunate to have the opportunities that I have had, my responsibility is to my family."
