Do my cats really know I exist? I wonder if my cat really knows me as an individual or just a mysterious connected object that somehow has hands and legs attached to a body. When I pet him, does he know that this action originates from my brain (head)? Or does he think that there is a mysterious soft massaging machine hanging in the air? Of course, most of us believe the former. Especially as he seems to be attentively looking into my eyes when I do so. But I wonder if there have been any rigorous scientific experiments verifying that? And from the Lex Fridman's interview of Christof Koch (47:47), he mentioned that bees have very complex neurons and can identify individuals. I also wonder how the experiment was done to verify that.
Although there is a robust science of animal behavior, it's very difficult to determine what kinds of experiences or thoughts animals are having. In short, we can only observe their behavior. Philosophers argue that a "zombie" or a robot could also demonstrate exactly the same behaviors but have no mind behind them, which means that we can't infer the thoughts just from the behaviors. We can't measure the thoughts themselves. Even neural activity is just a proxy; they are not the thoughts. Frans de Waal's recent bestseller goes into great depth on animal emotions and suggests that there are no uniquely human emotions; I'm guessing he would think that your cat understands you as an agent and has loving feelings towards you.  https://www.nytimes.com/2019/02/25/books/review/frans-de-waal-mamas-last-hug.html