In Fantastic Beasts: The Crimes of Grindelwald, we learn that
Nagini is a Maledictus.
Did Voldemort know about this?
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Though it may later be revealed that the Dark Lord did indeed know that Nagini was a Maledictus, there’s currently no indication that he (or anyone else) ever thought that she was anything other than a snake who was made into one of the Dark Lord’s Horcruxes. When we see into the Dark Lord’s thoughts through Harry, the Dark Lord thinks of Nagini as a snake - nothing more.
“He would visit the Gaunt shack first, then, and take Nagini with him: he would not be parted from the snake any more … And he strode from the room, through the hall and out into the dark garden where the fountain played; he called the snake in Parseltongue and it slithered out to join him like a long shadow …”
- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)
Furthermore, he mentally refers to her with the pronoun “it”, which would be an odd choice of words if he had thought that Nagini was once a human woman - though he doesn’t always respect them, he’s never called any of his human followers, either male or female, “it”.
Although there’s no indication that the Dark Lord thought of Nagini as anything more than a snake, he was a Parselmouth and could communicate with her, so presuming she knew and remembered her own history, he could have possibly found it out from her.
“After an interval of some years, however, he used Nagini to kill an old Muggle man, and it might then have occurred to him to turn her into his last Horcrux. She underlines the Slytherin connection, which enhances Lord Voldemort’s mystique. I think he is perhaps as fond of her as he can be of anything; he certainly likes to keep her close and he seems to have an unusual amount of control over her, even for a Parselmouth.”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
The had a mental link with Nagini, which was what enabled her to call him when she’d captured Harry for him, so it’d be theoretically possible for him to have known.
We would not know until JKR will tell her idea on that and given Nagini is a big part of the new story there should be some information in JKR's mind on how she end up with Voldemort. So probably we will learn that eventually.
Considering information we've got by now I would assume he should has known who Nagini was.
First, he could speak to her directly and he apparently has that special power Parceltongues have over snakes. So if he asked what she was, she would tell him. And, I mean, you do not just meet a giant magical snake without wondering what this thing is, where it's from and what it's capable of, do you? Especially as we know that Voldemort was very fond of the snake, as Dumbledore said to Harry:
I think he is perhaps as fond of her as he can be of anything…
We can not be sure though that on turning into animals for good maledictuses (maledicti?) preserve their human consciousness and memories. We don't really have any information on that so far. So Nagini would tell Voldemort her story if she remembered it herself.
But Voldemort could not only speak to her. He actually could posses her getting inside her mind. And from what Harry experienced it was not just like looking through her eyes, it was pretty much like being the snake and feeling everything she felt, sharing her thoughts as well. Given that Voldemort could do it I can't see how she could conceal anything from him.
So I believe that any bit of information Nagini had about herself she shared with Voldemort. The only question is how much of her past she still remembered by the time she had met him?