Holly Madison Names Daughter Rainbow
updated 03/08/2013 AT 03:30 PM EST
•originally published 03/08/2013 AT 03:00 PM EST
Holly Madison, 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 with motherhood.
"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!"