Credit: Michael Rozman/Warner Bros

Michelle's mommy quandary!

Michelle Williams' daughter Matilda Ledger turns 6 on Friday. But the Brooklyn-dwelling kid already got a major thing on her wishlist in advance of her birthday.

"We just got a puppy," Williams, 31, revealed during an appearance on The Ellen DeGeneres Show, airing Friday. "She's very into the puppy," which is a mixed "sort of spaniel thing," the Oscar nominee explained.

But a problem arose when the time came to name the canine cutie. "Her first ideas were...they sounded like stripper names!" Williams said. "She wanted something like, Crystal, Gem or Diamond."

The My Week With Marilyn star said she resisted the urge to be a "controlling mom...I was like, 'We can't have a dog named [that!]. But then I was like, 'You know what? Let her have it."

As it turns out, Matilda (whose father was the late Heath Ledger) settled on a less scandalous name: Lucky. "Which made me feel very lucky!" Williams cracked.

The acclaimed star also opened up to Ellen DeGeneres about her talked-about role as Marilyn Monroe in My Week With Marilyn.

"I spent the next 6 months trying to talk myself out of [accepting the part] because it was just so daunting," Williams said of learning to morph into the Some Like It Hot siren. "I was never really a very good student. I didn't go to school for a terribly long time. I think I'm making up for it now. I worked so hard. I read all the books. I watched the movies. I was obsessed with her. I woke up with her every morning and I went to bed with her every night, in a way."