As pointed out by others, you can't copyright a name. It would be trademarked. Disuse of a trademark generally renders it unenforceable as it no longer identifies any particular product or seller.
However, characters are copyrightable.
https://en.wikipedia.org/wiki/Nichols_v._Universal_Pictures_Corp if you're interested in that general subject. If they wanted to go after it, they'd have to argue the actual character is infringing on their specific character. It's a pretty shaky argument, and I'm pretty sure given the nature of such a suit that they'd have to prove this guy actually had knowledge of the original Cool Cat character, or make a probably flimsy argument that the character is so famous he had to have seen it at some point.
Since I'm pretty sure the character hasn't been used all that often or at all in recent decades, I think this would be difficult to show, and that other than just being anthropomorphic cats and the name, the characters have nothing to do with each other.
The character, such as it is, seems pretty generic, and is unlikely to be infringing a copyright, sort of like you couldn't copyright other generic characters, e.g., an "Irish town drunk" or a "Jewish mother" or other such stereotypes.
Obviously, if Derek has stated otherwise or there's more to the Cool Cat character than I know, it could be infringing. I just don't think it is on a casual glance.
