In both the film and the original novel, the second Mrs. de Winter is never given a first name. This is a deliberate creative choice by Daphne du Maurier, intended to emphasize how completely she is overshadowed by the "intense spectral presence" of the first wife, Rebecca.
While her name is never spoken, we are given a few specific clues about it
It is "unusual": Maxim tells her she has a "lovely and unusual name".
It is hard to spell: The narrator notes that early in their relationship, Maxim spelled her name correctly on an envelope, which she describes as an "unusual thing".
It came from her father: Maxim remarks that the name became her father just as well as it becomes her.
The Behind-the-Scenes "Name"
Interestingly, while the character remains nameless to the audience, the name "Daphne" (after the author) was often used by the cast and crew on set to refer to Joan Fontaine's character. In her autobiography, Joan Fontaine herself referred to her character simply as "I".
By keeping her nameless, the story reinforces her struggle with imposter syndrome, making her feel like a "placeholder" in her own life.

I strongly agree.
"You can't fight her - no one ever got the better of her. Never, never. She was beaten in the end, but it wasn't a man, it wasn't a woman. It was the sea!"

I think that is the most brilliant part of the movie. It show how much she is in the shadow of Rebecca and also that she- like we viewers- is given no name.

I like the mystery though, and the little references like when she says it is often misspelt. You almost never even notice that we don't know her name in the book since it is written in the first person narrative from her point of view.

There's rumours that in original drafts it was Daphne, which is the author's name. She says that it's uncommon and people often misspell it.

No. In fact, this has been a clue in crossword puzzles over the years, something like "movie in which we never learn the first name of the female lead." Now you know.

Someone on another site argued a case to believe it might be Mallory. Apparently the name signifies someone who is unfortunate (literally 'bad gold'). This was based on some text in the book where De Winter remarks that the name suits her character as well as that of her father, who was also unlucky.
I don't know if they have any real case there, but I thought I'd pass it along.

No, never. In movie or book(s).