According to Ladsbroke, the top favourite potential baby name is Arthur, which is the infant’s maternal grandfather, coming in at 5/1.
This is followed by James at 6/1 odds and Frederick, Edward and Albert at 8/1, while Hugo and Alfred are trending with 10/1 odds.
Given the negative publicity surrounding Eugenie’s father, Prince Andrew, it’s expected the princess will steer clear of Andrew, which is currently an outsider at 25/1
While early betting seemingly favours traditional names such as Arthur, Ladsbroke spokesperson Jessica O’Reilly said with Eugenie’s name being unique it could potentially influence her son’s name.
One left-field baby name that the online betting agency hasn’t ruled out is Tarquin – a boy's name of Latin origin.
Buckingham Palace first revealed the news of Eugenie and Jack’s first born in an official statement, which was shared to the royal Instagram account.
"Her Royal Highness Princess Eugenie was safely delivered of a son today, 9th February 2021, at 0855hrs at The Portland Hospital. Jack Brooksbank was present." The statement read.
"The baby weighs 8lbs 1oz.
"The Queen, The Duke of Edinburgh, The Duke of York, Sarah, Duchess of York, and Mr and Mrs George Brooksbank have been informed and are delighted with the news.
"This is Princess Eugenie and Jack Brooksbank’s first child, The Duke of York and Sarah, Duchess of York’s first grandchild, and the ninth great-grandchild for The Queen and The Duke of Edinburgh. Her Royal Highness and her child are both doing well."
The royal will now sit in 11th place on the line of succession, one place behind Eugenie and their extended family members.
As a result, the Queen’s youngest child, Prince Edward, 56, will be shifted from 11th to 12th place.