Despite the rich legacy of Prince Harry and Meghan Markle's daughter, both in name and heritage, "this little American girl is being brought up free of old-fashioned tradition," royal historian Robert Lacey tells PEOPLE

As she gets older, Prince Harry and Meghan Markle's daughter, Lilibet Diana Mountbatten-Windsor, will surely take rides on her dad's shoulders — but even now, the days-old newborn has a meaningful name that ensures she will stand on the shoulders of two of history's most powerful and influential women.

Lilibet (pronounced "LIL-eh-bet") is a name that "is given a name that carries this weight," royal historian Robert Lacey tells PEOPLE in this week's cover story.

"To be compared to the Queen, the most successful female monarch in British history, is a great weight," says Lacey. "It will be one of the first things that will be explained to her when she's old enough."

During a conversation with the Queen, Harry "shared their hope of naming their daughter Lilibet in her honor," a spokesperson for the couple tells PEOPLE. "Had she not been supportive, they would not have used the name."

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The Sussexes' friend Dean Stott tells PEOPLE, "Lili becomes the fourth generation of amazing, strong women in the family — behind Meghan, Diana and Her Majesty the Queen."

At the same time, since exiting their roles as working royals in 2020, Harry, 36, and Meghan, 39, have endeavored to give both their children space to blaze their own trails as they continue to deepen their own family roots in America and make a home in Meghan's native California.

"It is intriguing that this little American girl is being brought up free of old-fashioned tradition," notes Lacey.

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Diana Princess Of Wales & Prince Harry
Princess Diana and Prince Harry
| Credit: Julian Parker/UK Press via Getty

As for Diana, both Harry and his brother William have made sure their children know about their mother's legacy — which Harry will pay tribute to with a solo trip to London for the July 1 unveiling of the Kensington Palace statue honoring Diana.

In fact, 2-year-old Archie has a photo of Diana in his nursery, and among his first words were "Grandma Diana," Harry said in his mental health docuseries for Apple TV+, The Me You Can't See. "It's the sweetest thing," he said, "but at the same time, it makes me really sad because she should be here."

But now the family is focusing on feelings of joy with the arrival of baby Lili.

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"She is more than we could have ever imagined," the couple said in announcing the baby's arrival on their Archewell Foundation website on June 6.

"Harry and Meghan now have their complete family," says Stott. "It's their time to be in the moment.