How do pets (dogs, cats) recognize they are being called by their owner? How is it that they know their name or that they have a name?
Dogs do not recognize or understand their name in the sense that we recognize our own name. For dogs, a call name is nothing more than an auditory stimulus. They learn to respond to this stimulus because such responding is often followed by positive reinforcement of some kind - not just food, but attention, initiation of preferred activities such as going outside, and so forth. With enough repetitions of this contingency, the sound becomes a discriminative stimulus - a stimulus in the presence of which responding is likely to be reinforced. Such stimuli are all around us and serve the function of making the right behavior occur under the right circumstances.
When we say our dog's name and it responds in some way (looking at us, coming, etc.), their is no cognitive or mental or verbal "processing" involved. Unlike humans, dogs do not have the benefit of a verbal community that teaches a verbal repertoire that includes the learned skill of responding to our own behavior, which is part of what we call "recognizing." In other words, dog's merely respond to their environment, just as we do when we are not paying attention to our own behavior.
Our approach to understanding the behavior of dogs (or other vertebrates) is compromised by two traps. First, we tend to describe our dog's behavior in terms of what we assume to be human qualities. Even though the behavior of dogs and humans share many features, there are some key differences that should not be ignored. Second, we interpret canine behavior in terms of everyday dialect, which is chock full of mentalistic misdirection and misguided explanations. As with all natural phenomena, it is best to use the more technical and careful language of science in a search for description and explanation. The fundamental processes of operant learning that explain acquired canine behavior (as well as ours) have been thoroughly researched for many decades and are well understood.