The couple - who became proud parents on Tuesday - will have thought long and hard about what to call their bundle of joy, and our hunch is that Philip is almost certain to be included amongst the little tot's names.
The princess has an incredible relationship with her grandfather Prince Philip, who she affectionally calls "Grandpa," and it would be a beautiful tribute to him to name their son after him.
WATCH: Princess Eugenie and Jack Brooksbank welcome a baby boy
On his 99th birthday, she penned a touching message to him, along with two photos from her wedding to Jack in 2018, which featured the Queen and her husband.
She wrote: "A very Happy 99th Birthday to HRH The Duke of Edinburgh Grandpa, we wish you a special day… and may all grandparents celebrating birthdays in lockdown have a wonderful time #happybirthday."
She also shared a trio of sweet pictures of her beloved grandfather on his birthday in 2019 - one of which showed Prince Philip affectionately tapping his granddaughter on the head while she made her way to church.
"I found a couple of classic photographs of Grandpa and I on Christmas Day and Trooping the Colour a few years ago now," she captioned the sweet images.
Princess Eugenie is very close to her grandparents the Queen and Prince Philip
Eugenie has spent a lot of time with her grandparents and is also very close to the Queen - who is said to have a special bond with her sixth-born grandchild.
The new mother refers to the monarch as "Granny" and before COVID-19 restrictions, she was a regular visitor to their Scottish estate in Balmoral.
Eugenie called their home, "the most beautiful place on earth" in the documentary, Our Queen at Ninety, and added: "I think Granny is the most happy there. I think she really, really loves the Highlands… walks, picnics, dogs - a lot of dogs. There are always dogs.
She continued: "Family-wise we’re all there, so it’s a lovely base for Granny and Grandpa to be. For us to come and see them up there, where you have room to breathe and run."
The princess shared the first image of her baby on Instagram
Princess Eugenie and Jack announced their birth of their first child via a statement released on Tuesday afternoon. The statement from the Palace read: "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 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."
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