Any of those names are perfectly find to him. The name "Blackie" was one suggested for him, so his bar for creativity in names is pretty low.

When the bottlecap attempts to escape he finds himself biting it to keep it from getting away. He lets it go when he realizes what he's doing, since the game can't continue otherwise, but one fang has left a clear dent in the metal.

"I am always a cat," he conirms very precisely. Sometimes he is other things, but whatever he is, he is always a cat.