Kanye and Kim Kardashian West welcomed their third child, a baby girl, via surrogate on Monday

By Nicole Sands
January 17, 2018 06:05 PM

The couple, who welcomed their baby girl via surrogate on Monday, have yet to make a final decision on their daughter’s name.

“They still don’t have a name,” a source tells PEOPLE. “They’ve been thinking about it for months and they want to make sure it’s right.”

Adds the source, “They will get there eventually!”

On Wednesday, West, 40, confirmed that the couple — already parents to son Saint, 2, and daughter North, 4½ — are still trying to settle on a moniker when he was photographed arriving to work in Los Angeles.

“Can’t think of a name!” West told photographers, prompting one of them to suggest Donda after his late mother. The new dad of three, who was all smiles as he made his way into the office, laughed and responded, “Oh, that’s fire.”

Credit: Kim Kardashian West/Instagram

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Kardashian West, 37, announced the Monday arrival of her and husband West’s baby girl on Tuesday, sharing the new addition’s birth date, time and weight on her website.

“We are incredibly grateful to our surrogate who made our dreams come true with the greatest gift one could give and to our wonderful doctors and nurses for their special care,” she wrote, adding that Saint and North were “especially thrilled to welcome their baby sister.”

For more coverage, follow our babies magazine on Flipboard.RELATED: Kim Kardashian Celebrates Her Daughter’s Birth on Social Media: ‘#momofthree’

Later that day, the KKW Beauty mogul made her return to social media, celebrating her newest addition with a glam photo and the sweet hashtag, “#momofthree.”

“He’s so excited,” a source told PEOPLE of West shortly after the birth. “He said that being a dad is what he does best.”

The source continued, “He does everything that a dad does. Even diaper duty. Kanye knows how to change a diaper 100 percent! That’s very important to him.”