Melinda French Gates Shares the Sweet and Sad Story Behind Son Rory’s Name (Exclusive)

When it came time to think about a name for her son, Melinda French Gates knew she wanted to honor her late friend John Neilson.

In her new book The Next Day, the philanthropist, 60, writes about her friendship with Neilson, whom she met at Microsoft shortly after she’d accepted a job at the company. The two became fast friends, and would often hang out with their spouses — Melinda’s then-husband Bill Gates and Neilson’s wife, Emmy Ward Neilson.

“I once told John that next to our children and families, Bill and I considered our relationship with John and Emmy to be one of the most important things in our life,” Melinda wrote of her friendship with the Neilsons in her book. “The four of us came together right at the threshold of adulthood, and in a way, we grew up together.”

But things took a turn when Neilson was diagnosed with non-Hodgkin lymphoma. The cancer spread rapidly and Melinda, who was pregnant with her son at the time, wrote that she felt helpless. She visited John in treatment when she was still able to travel, but when he entered hospice care, she was “more than nine months pregnant.”

“The days that followed were restless and eerie,” Melinda wrote. “Any day now, my son would be entering the world. Any day now, my best friend would be leaving it. There was anticipation and dread, joy and grief.”

Once she and Bill decided that she would get induced, Melinda wanted to take the time to see John since she didn’t know how long she’d be in the hospital before she delivered — or if he’d still be alive when she got out. “I didn’t want to miss my chance to say goodbye,” Melinda wrote.

John didn’t have much energy for long visits, and Melinda said that their conversation was “short but wrenching.” She told him she loved him and that she “would be giving his name to my son.”

John didn’t die that night and in the book, Melinda wrote that the last photo she has of them together was taken on his own porch, where he’s sitting with her after she left the hospital.

Looking at picture now brings up a mix of emotions, but she wrote, “there’s joy in that picture, too, because on his lap, he’s holding my son, Rory Gates. Rory John Gates.”

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Reflecting on sharing this particular story, Melinda tells PEOPLE that “it’s hard even now” to talk about her friend’s death.

“That was really seminal in my life,” she says. “And yet I felt so good about the way I wrote that chapter.”

“I was like, ‘Will John feel like I wrote it in a true, authentic voice?’ Yes,” she adds. “And of course, I showed his wife and she didn’t ask me to change anything.”

The Next Day is available for preorder now.