Just so you know, Lovecraft was a very racist man. Now, Lovecraft did not hold all white people in uniform high regard, but rather esteemed the English people and those of English descent. He praised non-WASP groups (White Anglo Saxon Protestants) such as Hispanics and Jews; however his private writings on groups such as Irish Catholics, German immigrants and African-Americans were consistently negative. Just some food for thought.
The name of the cat, “■■■■■■ Man”, has often been cited in discussions of Lovecraft’s racial attitude. Lovecraft owned a cat by that name until 1904. The cat had likely been given its name when Lovecraft was about age 9.
HPL was known to have been fond of cats and owned several during his life.
That said, you’re probably asking about a particular name that he both applied to one of his cats and used as a cat’s name in one of his stories. The black cat in question, who either died or ran away in 1904, was named “■■■■■■ Man”
HPL was known to have extremely racist views (this is borne out in his correspondence and by contemporaries), and at least one reprinting of the story in question changes the cat’s name entirely.