"She wants to make sure North and Saint have a lot of extra attention and feel included as well," a source says about Kim Kardashian and Kanye West


Kim Kardashian West previously revealed that her daughter North got jealous of her little brother Saint when he first arrived into the family.

And following the arrival of their baby girl via surrogate on Monday, the Keeping Up with the Kardashians reality star, 37, and husband Kanye West, 40, are making sure both North, 4½, and Saint, 2, get some additional love.

“Kim wants to make sure North and Saint have a lot of extra attention and feel included as well. It’s a big deal for everyone to have a newborn in the family,” a source close to the new parents tells PEOPLE.

Adding, “Kim and Kanye are at home with the baby. They are so happy. They have had some visitors, but mostly Kris [Jenner] and Kourtney [Kardashian] are helping out.”

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Kim Kardashian and Kanye West with son Saint and daughter North at the KarJenner Xmas party in December
| Credit: Kim Kardashian/Instagram

Kardashian West revealed there has been a mini-rivalry between her kids, even before the baby girl’s arrival.

“I don’t know if it’s because she’s the older sister. I don’t know what it is. I thought it was a phase. She does not like her brother and it’s so hard for me,” she said in August while guest hosting with Ryan Seacrest with Live with Kelly & Ryan.

“She would get so jealous when I would breastfeed and all that kind of stuff. And now, the phase isn’t going away,” the mother of two shared.

WATCH: Kim Kardashian West Throws Cherry Blossom-Filled Shower for Baby Number 3

Couple months before, in June, Kardashian West gifted her eldest child a puppy, named Sushi, with hopes that caring for the pooch would teach North about responsibility.

“North has been asking for a puppy for a long time,” a source told PEOPLE at the time. “Kim thought it was a good idea for North to take care of a puppy. It could prepare her for a baby sibling too.”

Kim Kardashian with Saint and North in August
| Credit: Kim Kardashian/Instagram

As The Wests have expanded into a family of five, they have yet to make a final decision on the newborn’s name.

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

On Wednesday, the father of three confirmed they are still trying to settle on a name 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.”