Lauren Silverman, Eric and Simon Cowell
Courtesy of Simon Cowell
02/21/2014 at 11:00 AM EST
can now add "family man" to his already formidable résumé.
He and girlfriend Lauren Silverman welcomed their son
, Eric Philip, into the world last week, and Simon couldn't be more excited by his new job title: dad.
Cowell had such a tight bond with his own father, Eric Cowell, that he named his firstborn after him. He shared that inspiration over Twitter
, but Cowell's publicist and longtime friend, Max Clifford, tells PEOPLE just how close the music mogul was to his father.
"What he is striving for is to build the same relationship [with his son] over the years," Clifford says. "It's the whole family thing – he got a tremendous amount of comfort from the relationship he had with his mum and dad. They were very, very close."
Cowell has acknowledged how much of an impact being a father has already had on him, and he plans to follow in his own dad's footsteps. "He wants to recreate the father-son relationship that he got when he was a little one from his dad," Clifford says.
Eric Cowell passed away in 1999, leaving son Simon and his mom, Julie, grieving. "I know how upset he was and how much he missed his dad," Clifford says.