The judge ruled that giving your dog an offensive name like "N-word" is allowed under US law.
However, the lawsuit found that the Defendant named his dog N-word solely so that he could yell “N-word! N-word” in the neighborhood!
The South Park N-word guy episode
He lost the case, not because he named the dog "N-word", but because he did it to piss-off his black neighbors.
Evidently, naming your black dog “N-Word” is not a novel idea, but certainly not politically correct. Watch this clip from a British movie: