In "The Black Cat," one morning, the narrator decides to kill his pet cat by hanging it from its neck. This act of cruelty then plagues the narrator throughout the rest of the story, causing him to further lose his grip on reality. The cat's name is Pluto.
Pluto is the Roman god of the underworld and as such is associated with evil and death. The choice of Pluto for the cat's name, therefore, is a deliberate choice to symbolize the evil that the cat seems to inspire in the narrator and the evil that plagues the narrator after the cat's death. It is almost as if the narrator is dragged into the underworld, metaphorically speaking, along with the black cat.
One night, before killing his cat, the narrator seizes it in his arms. While holding the cat, the narrator says that the "fury of a demon instantly possessed him." He further says that his "original soul seemed, at once, to take its flight" from his body. The implication here is that the cat is perhaps a reflection of the narrator's own "fiendish" side and self-loathing, as the majority of the atrocities the narrator commits are "gin-nurtured," fueled by alcoholism and his own madness.
After a fire destroys his house save for one wall, the narrator sees upon it, "as if graven in bas relief," the exact image of his dead cat, Pluto, with a rope around its neck. Although he at first tries to reason away the impression, the narrator is, from this moment on, haunted by this "apparition." The memory of his dead cat plagues him. He later happens upon a second cat, which looks exactly like Pluto except for a patch of white hair that Pluto did not have. This second cat comes to be seen as like the spirit of the first, and it proceeds to torment the narrator:
At such times, although I longed to destroy it with a blow, I was yet withheld from doing so, partly by a memory of my former crime, but chiefly—let me confess it at once—by absolute dread of the beast.
Thus Pluto, in the form of this second cat, symbolizes the karmic return of the evil that the narrator first committed against it and from which he seems unable to escape.