I thought that it was the other way around. The planet came first, then the cartoon dog.
Uh... I think that was a joke.
I was joking, but your comment is interesting. According to Wikipedia, the name was first attached to the cartoon dog in "The Moose Hunt" (1931). Wikipedia continues as follows:
Several months had passed between the naming of what was believed to be the ninth planet, Pluto, on March 24, 1930, and the attachment of that name to the dog character. Venetia Burney (later Venetia Phair), who as an eleven-year-old British schoolgirl had suggested the name Pluto for the planet, remarked in 2006: "The name had nothing to do with the Disney cartoon. Mickey Mouse's dog was named after the planet, not the other way around."[12] Although it has been claimed that Disney named the dog after the planet, rather than after the mythical god of the underworld, this has not been verified. Disney animator Ben Sharpsteen said "We thought the name [Rover] was too common, so we had to look for something else. ... We changed it to Pluto the Pup ... but I don't honestly remember why."[13] Disney says they have no documents to support or refute the connection.[14][not in citation given] Unofficially, even Disney's animators believed that Walt Disney chose the name to capitalize on the sensation of the newly named planet.[15]