Matt Damon, George Clooney, Elle MacPherson, Thandie Newton, Helena Bonham Carter, and Tim Burton leaving the Harpers Bazaar dinner at L’Atelier in London, England, last night.

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Helena Bonham Carter and her partner, Tim Burton have finally chosen a name for their daughter: Indiana Rose.

Helena gave birth to their baby on December 15th, but have just recently decided on the name.

Sources say that they decided on the name just days ago. The reason for the wait? They originally thought they were going to have another boy.

It’s about time!!

Helena Bonham Carter and her director beau Tim Burton have welcomed their second child, PEOPLE has learned exclusively.

The infant, born in London late Saturday, joins big brother Billy, who is 4.

“They are absolutely delighted they have a daughter,” the actress’s rep, Karon Maskill, tells PEOPLE. “It’s a lovely Christmas present for the family.”

Bonham Carter, 41, and Burton, 49, have had a busy time of late. Both were nominated for Golden Globe awards for Sweeney Todd – she for best actress, he for best director. In fact, they got that news while at the doctor’s office.

“We were talking about inducing, and Tim got a call from his assistant,” Bonham Carter told PEOPLE before the birth. “I do look like a globe, so it’s kind of funny. I am very round.”

She also joked that it was probably hard on the baby while in utero to listen to Mom learning how to sing for her role in the musical. “Maybe the baby’s going to come out with his hands on his ears. ‘Shut up!’ ” she laughed.

She added that the anticipation of meeting the new baby was intense. “I just can’t wait,” she said. “It’s hard to imagine we can make anything other than Billy.”

The couple revealed the pregnancy exclusively to PEOPLE in August.

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Johnny Depp is hoooooooooooooooot.

Tim Burton likes to bring a touch of Halloween to the holiday season – the director always decorates his Christmas tree with fake dead babies and slime balls.

Horror fan Burton’s partner Helena Bonham Carter, who is pregnant with the couple’s second child, admits Christmas in their London home is a macabre experience.

She tells Playboy magazine, “It looks lovely and glittery from afar, and then as you get closer, you realize it’s rather gory.”

Tim Burton has signed a deal with the Walt Disney Co. to direct and produce 3-D movies based on Lewis Carroll’s “Alice in Wonderland” and his own short film “Frankenweenie.”

The “Alice” adaptation, combining live-action and performance-capture technology, will start shooting in early 2008.

Burton will then start work on a full-length version of his 1984 cult favorite “Frankenweenie,” about a pet dog who is brought back to life by his loyal owner in a very unusual way. The film will be shot in stop-motion animation.

Burton is putting the finishing touches on the Johnny Depp musical “Sweeney Todd,” which DreamWorks/Paramount will release domestically next month.

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