The name of Pluto is very metaphorical and allegorical in Edgar Allan Poe's short story The Black Cat. First, Pluto is the name given in Roman Mythology to the god of the underworld, or netherworld. This is a place presumed to be dark, mysterious, enigmatic, faraway, doomed, and cold.
Since Pluto was a black cat, one can assume that the main character chose to name him so in connection to the darkness that the god of the underworld, Pluto, inspires in the listeners. Since Pluto (the dwarf planet) was not named until 1930, there is no logic to suggest that it had anything to do with any celestial body nor any other Victorian scientific discovery.
Also, the main character felt suddenly possessed with the wish to do evil. He began to develop a borderline personality, nearly schizophrenic and sociopath where Pluto was his first intended victim. Then, as his insanity continued to develop, his hallucinations suggested him that Pluto was around avenging himself. In the end, we see the man may or may not have been possessed by the avenging spirit of Pluto.
Therefore, the mystery, evil, darkness, coldness and enigma that surrounds the story is directly moved by the character of Pluto and its effect on the main character. Pluto, the underworld is also a dark, evil, mysterious, and cold, enigmatic underworld. That may be the connection to which you refer.
The name Pluto has a connection to astrology in addition to mythology. I believe the connection to mythology is stronger in terms of this story. "The Number Eleven, this correlates to the Planet Pluto, the color of black, the sign of Scorpio, the Scorpion and Eagle the eighth house, and the letters K, & V. (V is a 22) 11x2" (Tribe, 2011)
Specifically the color of black is a direct connection to Pluto as this former planet was observed to be the darkest of the observed orbital spheres in the night sky.