What's in a name? Pink and husband Carey Hart welcomed daughter Willow Sage Hart into the world last month, and the singer revealed their reasoning behind her unusual name and how the new family is adjusting to their brand new baby.

"The willow is my favorite tree. I grew up near one. It's the most flexible tree in nature and nothing can break it - no wind, no elements," Pink told PEOPLE about the nature-inspired name for her little girl. "It can bend and withstand anything. I love that sentiment. I want that for her."

Her middle name also has a special meaning -- but Pink said it also just sounded cool.

"Sage is cleansing and sacred," she said. "And it sounded great together. It doesn't hurt that her last name is Hart -- flexible cleansed heart."

Though all is well with the happy family now, Willow gave her parents a hard time during her June 2 birth -- something that doesn't surprise the singer one bit.