Brainstorm

Nagini didn't willingly choose to become a ruthless killer for Voldemort, the tragedy of Fantastic Beasts is that she was an enslaved woman who simply ran out of time Nagini was a maledictus. That means that she carried an innate, hereditary blood curse giving her ability to transform herself into snake, which gradually became uncontrollable until Nagini eventually lost the ability to turn back into human completely. In the Fantastic Beasts: The Crimes of Grindelwald movie we see that Nagini was due to her curse treated like a freak and underbeing and forced to perform in a circus. It’s unknown how much of her human personality remained her in her snake form, so it is possible that after her permanent transformation she lost so much of her human self that there was only little to no difference between her and ordinary snake. After Nagini lost her ability to turn back into human she could have spent years, maybe whole decades trapped in the snake shape, during which was extremely lonely, because she didn't have anybody she could talk with as there wasn't anybody who could speak parseltongue. After such a long time she would have also started forgetting her memories and human traits naturally even if she kept them after the final transformation. All that loneliness, helplessness of being trapped in the snake body and gradual loss of memories could have been eventually so much mentally challenging that she could have eventually started to doubt whether she is indeed a woman trapped in body of snake or a genuine snake who was only dreaming about being a woman. It had to be an amazing surprise for her when she met Lord Voldemort who who could speak parseltongue and therefore was the first person in very long time she could talk with and as he was presumably the only parseltongue she ever met, she would be eager to do anything to befriend him, so she wouldn't be alone anymore. Lord Voldemort, on the other hand, would be interested in her, because he would surely consider her as an ideal companion, because he would see her snakiness and his ability to speak with her as another link to his ancestor Salazar Slytherin and as something he could use to support his atmosphere of dread and arcaneness. And don't forget that he could be very charming and persuasive when he wanted something. Then he reinforced Nagini’s loyalty to him by attaching part of his soul to her and making her a Horcrux. We also don't know when exactly Nagini and Voldemort met, however in the ending scene of Fantastic Beasts 2 we see that Nagini was member of the group visiting Dumbledore at the Hogwarts. It is possible that if Nagini stayed involved in fight against Grindelwald (maybe as one of few people Credence/Aurelius trusted) and kept visiting Dumbledore at Hogwarts she could have met and become close with young Voldemort when he studied there and that would later make it easier for him to convince her to join him.