Gigi Hadid Shares Her Cute Nickname for Daughter Khai, Plus Monikers for Baby's Grandparents

Gigi Hadid Reveals She Had a Home Birth — and Zayn Malik Helped Deliver Their Daughter Khai

Gigi Hadid tells Vogue she had to "dig deep" during the natural birth, adding that those in the room occasionally appeared to be "in terror"

Gigi Hadid has a super-sweet nickname for her baby girl.

On Thursday, a fan Twitter account for the model quickly went viral after claiming to have discovered the full name of the supermodel's daughter, Khai, whom she welcomed with Zayn Malik in September.

The Twitter account shared a screenshot of an Instagram comment left by Hadid, 25, in which she wrote, "I love u sm it hurts. Khaiba is lucky to have an auntie like you," and claimed to know the origins of the name "Khaiba."

Hadid later took notice of the tweet and cleared everything up, clarifying that "Khaiba" is "just a nickname."

"lol no it's just a nickname," she commented on the tweet.

In her recent Vogue cover story — in which she details her natural home birth and the joys of motherhood — Hadid also confirms the monikers she's using for Khai to refer to her grandparents.

Her father, Mohamed, will be Jido, which is "grandpa" in Arabic, and her mother, Yolanda, will be Oma, which is "grandmother" in Dutch. Malik's mom will be Nini, a variation of the British Nana, and his dad will be Abu, from the Urdu.

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

RELATED: Gigi Hadid Reveals She Had a Home Birth — and Zayn Malik Helped Deliver Their Daughter Khai

Yolanda, 57, gushed to the magazine about seeing her daughter become a parent, with the former Real Housewives of Beverly Hills star saying: "I'm proud of her face on a magazine, but seeing her give birth was a whole other level of proud. You go from looking at her as a daughter to looking at her as a fellow mother."

Hadid opened up to Vogue about having to "dig deep" during the birth, admitting she "knew it was going to be the craziest pain in my life, but you have to surrender to it and be like, 'This is what it is.' I loved that."

Want to get the biggest stories from PEOPLE every weekday? Subscribe to our new podcast, PEOPLE Every Day, to get the essential celebrity, entertainment and human interest news stories Monday through Friday. Get a taste of the podcast below.

RELATED: Yolanda Hadid Babysits Daughter Gigi's Newborn Girl as the Model Returns to Work

"There definitely was a point where I was like, 'I wonder what it would be like with an epidural, how it would be different,' " the new mom added. "My midwife looked at me and was like, 'You're doing it. No one can help you. You're past the point of the epidural anyway, so you'd be pushing exactly the same way in a hospital bed.' "

Since her daughter's arrival, Hadid has been giving fans glimpses of her baby girl on social media. She recently shared a sweet photo of the little one holding her finger, writing in the caption, "My girl!" Hadid has also offered fans details about her pregnancy, including the moment she found out she was expecting.