Mila Kunis' baby girl name: Ashton Kutcher's first child is finally here, but name remains a mystery

First-time parents Mila Kunis and Ashton KutcherTwitter/MilaKunis

The long wait is over for Ashton Kutcher and Mila Kunis, as the engaged couple welcomed their newborn baby girl Tuesday night at the Cedars-Sinai Hospital in California.

Entertainment website TMZ first broke the story.

TMZ reported that the couple went to the hospital at around 6 am on Tuesday, and Kunis was wheeled away immediately to one of the delivery rooms.

The former "That 70's Show" co-stars arrived by themselves at the hospital.

Earlier rumors suggested that Kunis wanted to give birth at home, but those were already debunked by the Gossip Cop.

However, Kunis shared her birthing plans with Ellen DeGeneres, saying that she wanted to have an epidural-free child birth if possible.

"The hospital that I'm going to be laboring in does a midwife, you know, doula type of thing," she mentioned. "I'm going to do it as all natural as I possibly can unless there's an emergency or something that should go wrong. I did this to myself, I might as well just do it right. I wanted this!"

The "Black Swan" actress had been preparing for the birth of their baby girl by attending prenatal yoga and Pilates. She was even seen coming out of her favorite yoga studio just days before she gave birth.

On the other hand, the first-time dad is also preparing for his daughter's arrival in his own way. Kutcher allegedly practiced driving his way to the hospital several times to make sure that they will have a hassle free transport once his fiancée is ready to give birth.

People also reported that Kutcher had been taking care of his future wife all throughout the pregnancy. "He's doting on her and telling her she looks beautiful. He understands she's going through changes and he hasn't judged her for it," a source shared.

The baby girl's name, as well as the other details of the childbirth, is still undisclosed at the moment.

However, several rumors were posted at SheKnows, saying that the couple is considering to call their daughter "Finn" which is taken from his mom's maiden name Finnegan. They might also give her a traditional Russian girl name just like what earlier reports had been speculating. 

Kutcher and Kunis announced their engagement last February, and the pregnancy news came around March this year.

The couple is excited to raise their little family together. The new mom told Marie Claire in an earlier interview that she and Kutcher want to make sure that they are raising their child the right way. She said, "I just don't want my kids to be assholes. I feel like so many kids nowadays are. Both of us just want to have well-behaved, honest, nice children who people meet and say, 'That's a good kid.'"