In “Romeo and Juliet,” the star-crossed heroine asks: “What’s in a name? That which we call a rose, by any other name would smell as sweet.”

People far less infatuated have wrestled with this concept for hundreds of years: How much should a name signify, and does it actually affect what or who a person is?

Meghan, Duchess of Sussex, would like a word.

In her new Netflix series, “With Love, Meghan,” the duchess, who is married to Prince Harry, told the actress Mindy Kaling that her last name was Sussex, correcting Ms. Kaling, who had referred to her by a more familiar name: Meghan Markle.

“It’s so funny, too, that you keep saying Meghan Markle,” Meghan said in the second episode of the series, which premiered last week. “You know I’m Sussex now.”

Meghan cited the importance of sharing a last name with her children.

“I didn’t know how meaningful it would be to me but it just means so much to go, ‘This is our family name, our little family name,’” she said.

Ms. Kaling, who initially seemed surprised, replied, “Well, now I know and I love it.”

It’s understandable that Meghan, whose representatives did not immediately respond to a request for comment, insists on usage of what she feels is the correct form of her name. But as with most Meghan-related news, the clip quickly made waves online as people took to social media to criticize her. Some commenters thought she was being pretentious, and others called her out for seemingly having confused her royal house with the family’s surname.

There was similar confusion over how to refer to the duchess after she and Prince Harry announced in 2020 that they would “step back” from their official royal duties and move to the United States.

Two days after the new series premiered, during an appearance on “The View,” Ms. Kaling said that she had “a great time” on the show, despite critics who felt like Meghan had behaved in a passive aggressive way toward her.

There is still some debate, however, on Meghan’s last name.

“She’s either totally oblivious to what her actual name is, she doesn’t understand it or she’s lying,” Hilary Fordwich, a royal family expert, said in a phone interview.

Ms. Fordwich explained that while it isn’t new for a member of the royal family to choose to go by their birth titles (Prince Harry went by Harry Wales during his time in the British army), that doesn’t make it their family name.

“By established protocol, he can use Harry Sussex, which I’ve never heard him use,” she said. “She could choose to use Meghan Sussex, but it’s not their surname. This was the issue in that Netflix clip.”

However, Rachel Bowie, the royals editor for the lifestyle website PureWow, didn’t think what Meghan said was problematic at all, adding that it’s “totally within royal protocol” and she didn’t see it as a formal change.

“Even though Archie and Lili were christened ‘Mountbatten-Windsor,’ Harry and Meghan are borrowing Sussex from their title to make up their last name,” Ms. Bowie, who was previously the co-host of the “Royally Obsessed” podcast, said in a phone interview.

“I never read it as Meghan formally changing her name, but more as this symbolic thing for herself, that she feels this connection, between the four of them, that they move through the world under the name Sussex,” she added.

Opinions have continued to roll in, even from relatives of Harry and Meghan.

Lord Ivar Mountbatten, a cousin of King Charles III and a reality television star on “The Traitors,” claimed she had been wrong about her own surname in an interview he gave to Town & Country, saying the family’s surname is Mountbatten-Windsor.

“Her children are called Archie and Lilibet Mountbatten-Windsor; they’re not called Archie and Lilibet Sussex, because Sussex is a title,” he said.

And Thomas Markle, Meghan’s estranged father, complained to the Daily Mail on Saturday about her decision to no longer use the name Markle, despite the fact that it’s still fairly common for a woman to adopt her husband’s name after getting married.

Understanding exactly how to refer to the royal family requires a look at its evolving history regarding names. According to the official website for the British Royal Family, “Members of the Royal Family can be known both by the name of the Royal house, and by a surname, which are not always the same.” It’s uncommon for core members of the Royal Family to be referred to by a surname at all.

Members of the Royal Family had no surname at all before 1917 and were referred to only by the name of the house or dynasty they belonged to. That year, King George V adopted Windsor as the name of the house and surname of his family.

In 1960, Queen Elizabeth II and Prince Philip, Harry’s grandparents, altered the name to distinguish their direct descendants from the rest of the extended Royal Family, making their new surname Mountbatten-Windsor, which included Philip’s family name.

“For the most part, members of the Royal Family who are entitled to the style and dignity of HRH Prince or Princess do not need a surname, but if at any time any of them do need a surname (such as upon marriage), that surname is Mountbatten-Windsor,” the site reads, using the abbreviation for His or Her Royal Highness.

Meghan now lives outside that structure, meaning those rules do not necessarily apply to her. So her choice to be referred to as Meghan Sussex, for now, will simply be added to the list of things she’s either criticized or embraced for.