When it came to choosing a name for her first child, Giuliana Rancic really wanted to name their son after his dad, Bill Rancic. Her husband, however, wasn't as into the honor.

"I've never been a fan of the 'junior.' I want to give him his own identity," Bill, 41, reasoned in a clip from the Nov. 13 episode of STYLE's Giuliana & Bill, filmed just prior to their baby's August 2012 arrival. "If he wants to name his son after me, then I've earned it."

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Considering names including Luke and Zach before settling on Edward, the couple agreed on the moniker to pay tribute to key influences in their lives: Their own fathers.

"Our fathers are great men -- your dad is Edward and mine's Eduardo. We could name him Edward," Giuliana, 37, says in the preview clip as the couple finally settle on what to name their boy. (Since his arrival, the couple has taken to calling him Duke -- his middle name -- which they picked because it means 'leader.')

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With his name selected, Giuliana then reveals that she most looks forward to having a constant reminder of the greatest man in her life: Her husband of five years. "I want to look at him and see you. I want him to be a 'mini Bill,'" she says on Tuesday's Giuliana & Bill. "Honestly, I want him to be just like you."

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Replies her optimistic husband: "He'll be better!"

Giuliana & Bill airs Tuesday at 8 p.m. (EST) on STYLE.

This article originally appeared on Usmagazine.com: Giuliana Rancic: Son Duke Is a "Mini" Version of Husband Bill