It's hard to imagine Blue Ivy Carter as anything other than Blue Ivy Carter, but her father, Jay Z, revealed that she was about to have a completely different name.

Appearing on CBS Morning's Gayle King, Jay Z said of his first daughter with wife Beyonce that her name "was going to be Brooklyn," in homage to her birthplace. However, during Beyonce's pregnancy, "I called her Blueberry. I was like, 'Look at little Blueberry. It was like a nickname. It was natural. I took the berry off and called her Blue."

Blue Ivy, who made headlines for appearing on nearly every show of Beyoncé's Renaissance World Tour, told Jay Z that despite some initial resistance, Blue finally realized how cool her father was and started asking for style advice: "Before, She was a little upfront about me," Jay-Z said in response to King's question about whether Blue thought he was cool. "But [now] I get her. Now she's asking me if this is cool, if her sneakers are cool." King asked, to which Jay-Z replied, "Yeah, yeah, yeah."

About taking the stage for the Renaissance World Tour, Jay Z said Blue "wanted to do it." Okay, if this is what you want to do, you can't just go out there. You have to go to work, with the dancers." The proud father nervously watched his daughter face the crowd with "goosebumps": "Blue was born into this world that I didn't ask for. ...... I was born into a life I didn't ask for. 'Ever since she was born, she's been in the public eye, and everyone has an opinion. I know how nervous she was. I know how scared she was. And she wanted to do it." Jay Z recalled that Blue wanted to perform on "opening night" and said, "She worked every day. Some days she had little icy patches on her back". He added, "So when she got on that stage, she got her strength back, and the song [she performed] is titled 'My Power.'"

As for his wife, "For me, this was her best tour," he exclaimed. 'It's really hard to compare them because they all have their different geniuses. But this tour felt the most complete to me."

In addition to Blue, Jay-Z and Beyoncé are also the parents of twins Rumi and Sir.