Actress Zoë Kravitz said that she once considered dropping the last name of her rocker dad, Lenny before she started her career, PEOPLE reports.

"I thought about not using it," she said . "I thought about just going by my middle name, Isabella, Zoë Isabella, and I kind of tried to do it, but it just like didn't stick. People kept on forgetting. No one was responding to this idea I had. I would tell my agent and it just wasn't happening."

While appearing May 4 on the Armchair Expert with Dax Shepard podcast, Kravitz, 31, said although she gave it thought, her father wasn’t thrilled about it.

"I also think I mentioned it to my dad at one point and I think I could feel that it made him a little sad," said Kravitz, whose mother is actress Lisa Bonet. "So, yeah, I just kind of stuck with it. I did used to be really insecure about people just associating me with my family and now I love it—I'm so proud of them and it's cool."