Jennifer Arnold, William and Bill Klein
04/26/2013 at 04:00 PM EDT
Becoming a family was always a dream for reality television stars Bill Klein and Dr. Jennifer Arnold of TLC's The Little Couple
. And now, mom gets to have a name in the house she's always wanted.
"When Jen and I met she started calling me Will," Klein tells PEOPLE, laughing. "I said, 'My name is Bill,' but at least for a weekend she called me Will until she finally gave up."
When the couple adopted their son William Rijin
, they already knew what his name would be when they welcomed him home to Houston, Texas.
"It is a family tradition that the oldest boy in Bill's family would be William Walter or Walter William," explains Arnold. "We can continue part of the tradition but also keep part of his Chinese name and so that's what we decided to do."
Little Will, who was originally identified on camera with the "fake" name Ben for confidentiality purposes, was born on Feb. 24, 2010, and came home with his new parents on March 5, 2013. Now he can look forward to celebrating both his birth date and his "gotcha" date, when he was adopted
"Jen loves to throw parties," says Klein. "I'm not a big fan of parties myself, but these are two days that I will be happy to always celebrate."
As he settles in to his new life, his happy parents are soaking up every moment of joy they can with him.
"I walk into a room and see him and I still can't believe he's ours," says Klein. Agrees Arnold, "We are so deeply in love with him already. It was meant to be."
The Little Couple
's new season premieres April 30 at 10 p.m. on TLC
For more details on Will's adoption and exclusive photos of the family together, check out next week's issue of PEOPLE magazine