You know PRECISELY why it's racist. The word cunt comes from cune/queen, but it's sexist because it's used to degrade women, regardless of archaic meaning. If the dog's name was Cunt, I would object.
Why in this particular case? The word has been used in countless mainstream films from 'The Green Mile' and 'Of Mice and Men' to 'American Gangster'. So much debate over the name of a dog?