09/05/2012 at 10:30 AM EDT
Just six days after Jersey Shore
star Nicole "Snooki" Polizzi and her fiancé Jionni LaValle welcomed their first child
, Lorenzo Dominic, they opened their home to PEOPLE to help introduce him to the world.
"It's a different kind of love that I never felt before," says Polizzi, 24, who is currently filming the second season of her MTV spin-off Snooki & JWOWW
It took more than 24 hours of labor, but the pint-sized reality star finally gave birth to her son on Aug. 26
. Happily, she and LaValle say that choosing a moniker was much easier.
"We were going back and forth, and I just happened to think of Lorenzo," says LaValle, 25, who adds that he was inspired by a child he knew from his hometown, where he and Polizzi now live with his parents. "She loved it."
The baby's middle name, Dominic, is in memory of Polizzi's uncle, who died. "I did it for my dad," she says.
Now, the happy couple are enjoying spending time with their family and of course, their "adorable" son.
"When I got pregnant, everything changed," says Polizzi, who will also appear on the final season of MTV's Jersey Shore
, premiering Oct. 4. "The partying is long gone. I'm a new person."
For exclusive photos of Lorenzo – plus details about Polizzi's delivery, upcoming wedding, weight loss plan and life as a mom – pick up this week's issue of PEOPLE, on newsstands Friday