April 19, 2016 07:45 PM

They said they weren’t going to “hide” their daughter from social media, and five days after welcoming baby Luna SimoneJohn Legend and Chrissy Teigen have shared the first photos of their newborn, along with her nickname.

“Hi my lulu!” the first-time mom captioned an Instagram photo of herself with Luna. Legend’s image was captionless, allowing his daughter to take center stage.

Wearing a black bra and leggings, Teigen, 30, held her daughter in one arm while rubbing her head as she was also joined by her mother Vilailuck Teigen. “Lulu and me,” the proud grandmother captioned her own photo.

Chrissy Teigen/Instagram

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Teigen also shared her thoughts on some of the less glamorous aspects of post-delivery life, tweeting, “No one told me i would be coming home in diapers too.” She later added a photo of a perineal irrigation bottle, captioning it, “Buying myself a push present … have you EVER heard of a grosser name for a product, EVER???”

The Lip Sync Battle star and her musician husband, 37, welcomed their first child on Thursday, they announced via social media.

“She’s here! Luna Simone Stephens, we are so in love with you!” Teigen tweeted alongside a snapshot of the baby’s weight.

Fans can hopefully expect more Luna updates in the future, as the new mom previously told PEOPLE that she and Legend aren’t hesitant about what to share when it comes to social media.

“I am conscious of what people want to see and what they don’t want to see, or what they see through completely,” she shared with PEOPLE exclusively in March while chatting about her book Cravings.

“We’re not going to go out of our way to hide because obviously it’s such a big part of our lives to show everything: the inside of our homes, my parents living with us, our animals, everything,” the then-pregnant star said of the couple’s social media strategy. “I’m not going to do sneaky back shots of her or anything.”

— Karen Mizoguchi

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