Oh, geez, the cat's name is never, ever ok. Nor are the bankers in Harry Potter (nor Rowling's transphobic comments - but don't get me started on that...)
Let me elaborate on the process of cutting the cord, since I could have done a better job of explaining it above.
For me, the difference comes from the source of interpretation. If the ultimate meaning of the story is determined by Lovecraft, then the cat's name is just a trope of racism because his was a racist worldview. But "death of the author" implies that meaning comes to rest with the reader (or, as I would probably argue, some combination of the author and reader). As a reader, I can recognize the awful name and ask myself what the name tells me about the time of the narrative, the place of the narrative, the metaphors employed in the narrative, the mistakes revealed in the narrative, etc. (including what the name tells me about the author - whether or not he was conscious of it or wanted to be seen in that light, because sometimes our creative work shows hidden aspects of our personalities). In this sense, I can view the story as interesting and worthy of analysis even if the author was a royal sphincter - not because he was a racist, but because I'm not (and, therefore, I get to make my own meaning of that cat's name, that it's horrible and tells us about a horrible time and place that we must transcend). If the (my) meaning of "The Rats in the Walls" overpowers Lovecraft's, then the story has been redeemed in the sense that I recognize it contains something that is (to me, anyway) irredeemable. The story has become an extension of my worldview, wrested (at least in part) from Lovecraft's - and that's a worldview that admonishes the cat's name instead of celebrating it.
And, yes, we have to consider who profits off of certain works - and do the responsible thing in making sure we don't pay to consume them.