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

Isla and fiance Sacha, who welcomed their first child into the world in Los Angeles last Wednesday, 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."

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