“Kim is just so thrilled that her dream of having three kids finally came true,” the source said. “She’s really enjoying these few days just being with the baby and her family and soaking it all in.”
Adding, “She was a little nervous about how Saint and North would react but so far everything is great.”
Want all the latest pregnancy and birth announcements, plus celebrity mom blogs? Click here to get those and more in the PEOPLE Babies newsletter.
An insider previously told PEOPLE that the couple’s 4½-year-old daughter and 2-year-old son have been receiving “a lot of extra attention” and “feel included” in the celebration of their little sister.
On Friday, Kardashian West finally revealed the name of their baby girl four days after she was born via surrogate on Jan. 15.
While the mother of three did not give an explanation behind the name choice, Kanye, notably, was raised in Chicago and frequently pays homage to his hometown in his songs.
“I LOOOOOOOOOOVE her name. Hey Chi (shy),” she tweeted with the pronunciation of the newborn’s nickname.
While Kim and Kanye may not have given any distinct clues ahead of the name reveal, brother Rob Kardashian may have dropped a hint. On Wednesday, he tweeted two (Chicago?) bear emojis.
One family member who may have contributed to the selection of Chicago’s name: big sister North, who was tasked with the responsibility shortly before the birth.