Since the picture was posted there, have been rumours that a well-meaning friend had revealed the bub's name.
In the comment section of a black-and-white photo of Buddy proudly holding his newborn son, which was shared on March 24 in celebration of his birth, the footy star’s friend fashion director, Justin O’Shea, commented, “Rocky,” paired with clapping and a heart emoji.
Jesinta has been settling in well as a new mother of two, and she has given fans hints into her world on her Instagram.
Last week, she shared a touching photo of Buddy kissing his kids goodbye before he headed off to play an AFL match.
"Game day prep looks a little different in the Franklin household these days and we wouldn't have it any other way We love you @buddy_franklin23 . Great win today @sydneyswans," she penned next to the snap.
Meanwhile this week she posted a photo of her son's feet and simply mused: "So in love."
The 29-year-old model confirmed her second pregnancy in October last year during an Instagram live session with Vida Glow founder Anna Lahey.
"It was a very big surprise for us. Tullulah will be getting a sibling at the end of March next year so she will have just turned one," she explained at the time.
''I'll have a 13-month and a newborn, which was very daunting at first."
Despite taking four years to fall pregnant with Tullulah, Jesinta admitted the second time around was much easier with the couple finding out they were expecting just a week after Buddy travelled up to Queensland to be in the AFL hub.