"That's the next bit," Prince Harry, 34, said in brief remarks Monday near Frogmore Cottage, the Windsor home where he and Meghan will raise their son.
When Buckingham Palace confirmed Monday that Harry and Meghan's baby is a boy, the oddsmakers quickly began placing their bets on which name the couple will choose.
The name Arthur is currently in the lead, followed by Alexander, which has been "by far the biggest mover" since the birth announcement, according to Ladbrokes, a London-based betting and gambling company.
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Albert, James, Alfred, Philip, Thomas and Spencer are also among the names that round out the top list, according to Ladbrokes.
Harry, and Meghan, 37, may follow in the royal tradition of giving their child several middles names. Harry's full name, for example, is Henry Charles Albert David.
Unlike the children of Prince William and Kate, the Duke and Duchess of Cambridge, Harry and Meghan's baby will not automatically carry the title of prince. Harry's grandmother, Queen Elizabeth II, does have the discretion to issue his child a title.
Here is what to know about the meaning behind the names that are among the current favorites for Harry and Meghan's son.
Arthur: The name Arthur goes way back in the history of the royal family, from the legendary king of Camelot to Queen Elizabeth II's father, King George VI, who had Arthur as a middle name (Albert Frederick Arthur George).
Harry's father, Prince Charles, brother, Prince William, and nephew, Prince Louis, all also have Arthur included in their names.
Alexander: Alexander is a name steeped in tradition for the royals. William and Kate's oldest son, Prince George, has Alexander as one of his middle names.
Queen Elizabeth has Alexandra, the female version of Alexander, in her name and one of George the First's daughters was an Alexandra.
Edward VII and Queen Alexandra, Queen Elizabeth II's great-grandparents, named their sixth child, who died shortly after birth, Prince Alexander John Charles Albert of Wales.
Albert: Prince Albert married Queen Victoria in 1840, three years after she became the Queen of England. Albert, a father of nine, is remembered for his contributions to the arts in the U.K.
He was an "enlightened patron" of music and served as President of the Fine Arts Commission, among other patronages, according to the royal family's website.
Prince Harry's full name is Henry Charles Albert David.
Philip: Philip would honor Harry's grandfather, Prince Philip, 97, the longest-serving consort in British history.
None of William and Kate's three children have Philip in their names so it could be one that Harry and Meghan opt to use.