Willis said on "The Late Show with David Letterman" that "She wanted me to mention here on the big show that she's legally changing her name from Talullah to Lula, just Lula. She doesn't like her name."
Willis has agreed to let his daughter go through with her plans -- because he knows what it's like to grow up with a name you don't like. He adds, "I didn't care for my name. ... especially after my father told me that he named me after Bruce Wayne, Playboy millionaire."