Baby Lilibet's Name Proves 'Remarkable Bond Between Harry and His Grandmother,' Says Royal Historian

The name Prince Harry and Meghan Markle chose for their firstborn daughter is as powerful as it is personal.

To her father especially, Lilibet Diana Mountbatten-Windsor's name reflects the unbreakable bonds Harry feels with the two women who have made the strongest mark in modern royal history: his late mother, Princess Diana, and, of course, his beloved grandmother, Queen Elizabeth.

The name also signifies the closeness that endures between Harry and the Queen - even amid the ongoing tensions Harry, 36, has addressed with "The Firm" and "The Institution" (as he has labeled his family's complicated dynamic in reconciling their personal relationships with their roles as public figures).

"The remarkable bond between Harry and his grandmother" has been a critical, royal historian Robert Lacey tells PEOPLE exclusively in this week's cover story.

Steve Parsons - WPA Pool/Getty Queen Elizabeth and Prince Harry in 2019

Tim Graham Picture Library/Getty Queen Elizabeth and Prince Harry

After the 1997 death of Princess Diana, the Queen "was a sort of stepmother for both Harry and William," says Lacey. "We have all focused on her coaching of William as the future King, but we are realizing now the importance of the emotional bonds that she's been able to establish with Harry and their ability to talk to each other directly. That affection remains."

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."

Queen Elizabeth was also among the first to meet baby Lili! A source tells PEOPLE that the Queen joined the Duke and Duchess of Sussex on a video call as soon as they returned home from Santa Barbara Cottage Hospital, not far from the family's home in Montecito, California, because they "were very excited and couldn't wait to share that their daughter arrived."

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And just like her older brother Archie, 2, Lili will come to know not only her extended royal family, but also their rich legacy and that of the immeasurably important great-grandmother after whom she is named.

"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."