Hilary Duff says son Luca discovered she's famous

June 19 (UPI) -- Celebrity mom Hilary Duff says son Luca recently discovered she's famous.

The 29-year-old actress confessed on Monday's episode of Good Morning America that she "didn't know how to respond" after the 5-year-old learned she's a star.

"I picked him up from school and when we got home he's like, 'I know your name,'" Duff recalled. "I was like, 'I know.' He's like, 'No, no. Your name's Hilary Duff.' I was like, caught! I didn't know how to respond. I'm like, 'Yeah, that is my name.'"

"He said it with a little glint in his eye, like somebody told him something that I haven't," she added. "I was like, no, I'm not ready for this yet! He's seen me on the cover of a magazine before in the grocery store, but I think he thinks that the next day it's the next mommy's turn to be on it."

Duff shares Luca with ex-husband Mike Comrie, from whom she split in 2014. She said in the April issue of Cosmopolitan that she has adjusted to co-parenting with the 36-year-old retired NHL player.

"Some of my friends tell me, 'God, it must be so nice, you get a break from your kid because you share him.' I'm divorced, and it sucks. Well, it did suck for a while; now it's just normal," the star told the magazine.

"But it's true, I do get a break," she qualified. "I had Luca by myself for a few weeks, no help, when Mike was on the road, and when he got home I was like, 'He's yours! Bye!'"

Duff plays Kelsey Peters on the TV Land series Younger, which will return for a fourth season June 28. She shared a photo on Instagram of herself with Luca last week.

"Le goof troop," the actress captioned the picture.