Isla Fisher and Sacha Baron Cohen have named their newborn daughter Olive.

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Isla and fiance Sacha, who welcomed their first child into the world in Los Angeles last Wednesday (17.10.07), are said to have finally agreed on the baby’s name.

A source said: “Isla and Sacha are over the moon with their newborn daughter. They wanted to wait until they saw the baby to pick a name. Both agreed Olive is perfect for her.”

Borat star Sacha is “thrilled” with the new arrival and has been a hands-on dad since the birth.

The couple’s representative said: “They had a beautiful healthy baby girl. Mother and daughter are doing great.”

Isla accepted Sacha’s marriage proposal in 2004, although they are still to set a wedding date.

The Australian actress – who converted to Judaism for Jewish Sacha – recently insisted she has no plans to follow in the footsteps of many other celebrity mothers and throw herself back into work.

She said: “There is no way I am going to worry about missing out on work or the pressure to lose weight. At the moment I am not even planning any work.”