The Queen approved of Lilibet's name
Lilibet was the childhood nickname of Queen Elizabeth and only a few in her inner circle referred to her by the monicker. Meghan Markle and Prince Harry named their daughter Lilibet Diana after her paternal grandmother and great-grandmother. In his new book Elizabeth: An Intimate Portrait royal biographer, Gyles Brandreth a friend of Prince Phillip writes that the Queen was flattered by her great-granddaughter's name but other members of the royal family were not.
In the book, Brandreth also claims that Elizabeth II was fond of Markle which seems to confirm Meghan saying that the Queen always treated her with kindness despite rumors to the contrary. The Duchess of Sussex probably would not have named her daughter after the monarch if the two had a frosty relationship.
Lilibet was born after Prince Harry and Meghan Markle moved to the United States and rumors were flying that there was bad blood between them and the royal family. This is why the child's name raised some eyebrows. with the public. Brandreth claims that (unnamed) members of the royal family found the name to be "bewildering and somewhat presumptuous." The Queen, however, said the name was “very pretty and seems just right.”
The royal naysayers might be jealous
In his book Branddreth says that Prince Harry stated that he obtained his grandmother's permission to name his daughter after her but the Queen said Harry told her he wanted to name ‘Lilibet’ in her honor and she accepted their choice with good grace, taking it as the compliment it was intended to be.” No one had any issues with Meghan and Harry naming their son Archie Harrison Windsor Mountbatten but the Queen obviously was considered to be off limits when it came to naming children.
There also might have been some royals who believed naming the child Lilibet was in poor taste because Prince Harry and Duchess Meghan were perceived to have turned their backs on the Queen when they walked away from being full-time working royals. There is also the possibility that some members of the royal family were upset with the Sussexes decision because none of them thought to honor the queen when naming their own children.
Prince Andrew's daughters are Princess Beatrice and Princess Eugenie. Princess Anne's daughter is Zara Tindall ( no title). Prince Edward's daughter is Lady Louise Mountbatten Windsor and Prince Wiliams' only girl is Princess Charlotte. In the end, if the reigning monarch for 70 years was flattered to have her granddaughter named on her behalf then no one else should have had any issues with the name. Queen Elizabeth and Princess Diana are gone but their names Lilibet Diana live on into a third and fourth generation.