The former Olympian revealed her new name and appearance on Monday
Credit: Vanity Fair

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Caitlyn Jenner made her big debut on Monday, appearing for the first time as a woman on the cover of Vanity Fair.

Formerly known as Bruce, Jenner introduced the world to “her” after months of speculation – though the 65-year-old former Olympian’s new first name has reportedly been with her for a long time, a source close to Jenner told PEOPLE on Monday.

“The name is what he always loved when he thought about this [female] part of his life,” said the source.

Jenner initially wouldn’t reveal her new name to Diane Sawyer during her emotional 20/20 interview in April, saying, “The media would go crazy.”

At the time, Jenner still wished to be called Bruce and to be referred to using male pronouns.

“He’s been answering to Bruce for so long. It’s like, ‘Let me do this at my own pace. Hear my words first, my story and have some context for this,’ ” Mary Andres, an associate professor at the Marriage and Family Therapy Program at the University of Southern California told PEOPLE in April.

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PEOPLE first shared the news that Jenner would be covering Vanity Fair on Friday. Famed photographer Annie Leibovitz shot the images of the Keeping Up with the Kardashians star for the magazine’s July issue, in which Jenner asks fans to “Call Me Caitlyn.”

“That’s been his name since he was a kid. I’m almost sure,” the same source told PEOPLE.

The American spelling of the Irish name Caitlin, Caitlyn means “pure” – a fitting sentiment for the woman who told Vanity Fair that she considers the cover reveal the moment when she is finally “free” – and a source tells PEOPLE Jenner’s children have been calling her by this name for some time now.

Jenner will continue to chronicle her new life as Caitlyn in an eight-part docuseries premiering July 26 at 9 p.m. ET on E!

With reporting by JENNIFER GARCIA