A weird amount of people I knew growing up named their cats just "cat" or "kitten". Every dog had a name (even in households that had a "cat" cat) but not all cats. I wonder if the cats figure their own names out in these cases :)
I grew up in a house of at least a dozen cats. All had names. Our very first one, Lightning (who was seemingly very intelligent and lived to his late teens), did not know his name as Lightning. For all he knew, his name was Puss-Puss, because he had been called that a lot when he was younger, and responded extremely well to it throughout his life.
That's how I grew up. We always called them "cat" or "kitty" and would get more specific as needed and based on how we felt about them at the moment. Anything from "the cute black one" to "that orange fool."
We were always told that no one really owns a cat, but we should take care of them all because it's good luck.
My last cat was with me for 20 years and neither of us seemed to feel the need for a name. We both knew who he was, and why bother beyond that? I think the difference is that dogs who live with humans tend to look to us to help them understand who they are, while cats never want telling no matter how close the association.
I didn't use the "pet voice" with him, either. Dogs, sure, but generally when I have something to say to a cat I say it like I would to a human, and that seems to mostly work okay.
That said, I find as with dogs that cats respond more to pitch than to content; I'm not sure their theory of mind for us extends far enough to recognizing that we also have language, but they certainly do learn some of the sounds we make.
When I needed him to come find me, I'd whistle just above the highest pitch I could hear, and he came running because I'd taken care to associate that sound with treats in his kittenhood. As his hearing range contracted in his dotage, I switched to the more usual "pspspsps" sort of sound, which worked about as well.
Granted, I grew up with cats, and my mom was of a mind that the best way for me to learn their style of manners was to let them teach me directly. This worked well enough that it's long since ceased to be a surprise when someone says something like "but our cat doesn't like anybody!" So I don't know how well my experience is likely to generalize.
Probably says a lot about how much brutality we've engineered out of daily living. I recall having a visceral reaction to hearing about the kittens as a child, and I imagine it's fairly natural to feel that way. I'm glad I lived in a time and place where that kind of desensitization wasn't necessary.
Unfortunately it is still fairly common in small villages (in Hungary at least - which is quite poor outside of its capital). Spaying is expensive and cats do produce plenty of offsprings, and it is not even like with dogs that you can just keep inside the backyard..
(Though what I heard about is not drowning, but slamming them hard to something :/)
