Well sort of.
Although she doubts she’ll get partner Kayne West’s approval, Kim, 35, admits she quite likes the name Easton, or Easton West, for her new son.
“It’s definitely not South but I do like the name Easton,” she confessed to Ellen a few weeks back.
As her 53 million Instagram followers hold their collective breath, social media is alight with conjecture on the most likely moniker for North’s new sibling.
The leading candidate so far? If you ask the Twitter-sphere there’s no contest – it’s EastonWest by a street.
The baby name hashtag is now so popular that people are now assuming it really is the official one.
Either way, Us Weekly magazine is confident she’s planning to pay tribute to her late father Robert Kardishian with the new arrival.
“I know they were doing Robert for the middle name in honour of her father,” says the report.
The famed O.J. Simpson lawyer – who Kim’s younger brother, Rob, is also named after – died of cancer in 2003, at the age of 59.
Meanwhile, the only word from inside the normally media-friendly Kardashian fishbowl is this Twitter pic below.
“He’s here! Kim tweeted just a few hours after her new son’s safe arrival, along with a sweet snap of her and Kayne, 38, holding hands.
Kardashian ‘momager’ Kris Jenner paid a visit to her new grandson 24 hours after Kim and Kanye announced the arrival of their second child.
The 60-year-old was seen for the first time arriving at Cedars-Sinai Medical Center in Los Angeles where Kim is in an exclusive $4000-a-night maternity suite.
Kim has already had several family members visit. Khloe was spotted arriving earlier on the day of the birth and People magazine reports that her other sister Kourtney assisted Kim throughout her labour.