Lily-Rose Depp has no desire to be famous and will do anything to protect her privacy.

The actress, daughter of Johnny Depp and French singer and model Vanessa Paradis, has recently carved a place for herself in Hollywood, thanks to her roles in HBO’s The Idol and director Robert Eggers’ Nosferatu. However, she recently opened up to The Daily Telegraph about the importance of preserving her anonymity in this industry.

“Every job comes with a set of circumstances and this [fame] is kind of one of them,” she explained. “The importance to me has been to maintain a sense of, like, privacy and grounded-ness and to protect [what] really belongs to you.”

It’s been a decade since Depp made her first onscreen appearance in 2014’s Tusk. Since then, she’s continued to rise in fame, appearing in more than a dozen projects. And though she watched her parents navigate the industry while growing up,...