The couple revealed their newborn son's name on Saturday

Princess Eugenie and Jack Brooksbank paid tribute to their family when choosing the perfect name for their newborn, son August Philip Hawke Brooksbank.

The couple, who welcomed their first child on February 9, revealed their son's name on Saturday, which includes a loving nod to Eugenie's grandfather, Prince Philip.

"On his grandfather's birthday weekend, thinking of my grandfather, we are introducing our little boy," Eugenie, 30, wrote on her Instagram Story, referring to both her father, Prince Andrew, as well as the Duke of Edinburgh, who is currently in the hospital for "observation and rest" after "feeling unwell," according to Buckingham Palace.

"He is named after his great grandfather and both of his great x5 grandfathers," Eugenie added alongside a sweet family photo.

Prince Philip, Princess Eugenie
Prince Philip, Jack Brooksbank and Princess Eugenie with son
| Credit: Samir Hussein-Pool/WireImage; Princess Eugenie and Jack Brooksbank via Getty Images
Jack Brooksbank, Princess Eugenie and son
Jack Brooksbank, Princess Eugenie and son

In addition to the sweet tribute to Philip, 99, the couple also chose to honor one family member from Eugenie's side and another from Jack's.

The baby boy gets his first name from Queen Victoria's husband Prince Albert, who was born Franz Albert August Karl Emanuel. The name August means "great, magnificent."

The rest of his moniker comes from a 5x grandfather on Jack's side, Rev. Edward Hawke Brooksbank.  

Princess Eugenie
Jack Brooksbank, Princess Eugenie and son
| Credit: Princess Eugenie Instagram

While introducing their son to the world on Saturday, Eugenie shared three photos of the couple holding their son. In the images, Jack coordinated with baby August in a blue sweater while new mom Eugenie wore a cream-colored dress.

"We wanted to introduce you to August Philip Hawke Brooksbank," Eugenie captioned the post. "Thank you for so many wonderful messages. Our hearts are full of love for this little human, words can't express. We are excited to be able to share these photos with you." 

RELATED VIDEO: Princess Eugenie Shares Adorable First Photo of Her Newborn Son on Instagram

Sarah Ferguson also shared a sweet post in honor of her grandchild, whom she called a "beautiful blessing."

"As Grandparents, The Duke and I are thrilled and blessed at the arrival of our grandson August Philip Hawke Brooksbank," she wrote on Twitter.

"He is a beautiful blessing and a bringer of such love and joy to all our Family. I am so proud of Jack and Eugenie, they are and will be wonderful parents," she added.

The couple welcomed their son on Feb. 9, and posted the very first photo of their new family of three shortly after the birth.

Eugenie is "doing really well" after having a C-section due to her previous spinal surgery for scoliosis, a source who has spoken to the new mom since the birth tells PEOPLE in this week's issue.

Can't get enough of PEOPLE's Royals coverage? Sign up for our free Royals newsletter to get the latest updates on Kate Middleton, Meghan Markle and more!

The source adds that Eugenie "sounded very content and said the baby is a complete dream!"

The baby is the ninth great-grandchild for Queen Elizabeth and Philip and first grandchild for Eugenie's parents.