A number of favourites emerged soon after the couple revealed they were expecting last fall, and they've stayed near the top choices for bookies. Betting agencies Betfair and Ladbrokes have Arthur as the number one pick, with 5/1 odds at the latter. James is second at Ladbrokes, coming in with 6/1 odds, while Frederick, Edward and Albert are tied for third at 8/1.
Godfrey, Henry and Thomas are also favourites at Befair, with the latter taking 14/1 odds, while the two former names sit at 10/1.
A Hello! Canada poll revealed most of our readers think that Philip will be the baby's name. Alexander, James and Oliver were second, third and fourth in polling.
It seems very likely the name Philip will be included in some way, whether as the little lad's first name or one of his middle names. It would be a lovely tribute to Eugenie's grandfather, the Duke of Edinburgh, who turns 100 this year.
While the top name picks from our readers and those placing their bets pay tribute to the Royal Family's history, Ladbrokes pointed out that the couple may opt for something entirely different. Indeed, many recent royal babies have had names that aren't traditional, such as Archie, Savannah and Isla Phillips and Mia and Lena Tindall.
"Given Eugenie's name we can't rule out something little more out-there, such as Tarquin or Humphrey," Ladbrokes' Jessica O'Reilly said in a statement.
When we'll hear about the baby's name is also up in the air. Prince Harry and Duchess Meghan revealed Archie's name on May 8, 2019, two days after he was born. Prince William and Duchess Kate waited the same amount of time to share Princess Charlotte's name with the public, while Prince George's name was announced the next day. Prince Louis's name was revealed four days after he was born.
But there's great variance in terms of when announcements have been made, even closer to the throne. The Queen took a month to reveal Prince Charles's name, and Sarah Ferguson and Prince Andrew did not announce Eugenie's big sister Princess Beatrice's name until two weeks after she was born in 1988.
Congratulations to Princess Eugenie and Jack Brooksbank!