Holly Madison and Pasquale Rotella
Courtesy Holly Madison
03/08/2013 at 03:30 PM EST
Now she's the mom next door.
, who gave birth to a daughter
on Tuesday, has chosen a name for her baby girl: Rainbow Aurora Rotella.
"I wanted to give my daughter a unique name," she explains to E! News
, who first reported the news.
"Growing up, there was a girl in my school named Rainbow and I was so envious of that name. I thought it was so pretty and unique!"
The former Playboy Bunny seems to be seriously smitten
"I've been spending the last day or so learning how to be a mom – it's the best project in the world," the former Girls Next Door
star wrote on her blog
Friday, underneath a makeup-free photo of her and boyfriend Pasquale Rotella
leaving the hospital. "I never thought I would be so happy – especially on so little sleep!"
Cuddled up with a stuffed animal and a pink-themed ensemble, the reality star acknowledged her fans for their support in becoming a first-time parent.
"I just wanted to say thank you for all the wonderful messages you guys have been posting!" she wrote. "I appreciate them all!"