Your example of the leash and the concept of "walking" is an excellent point.
To answer your question, all proper nouns are not abstract by definition. Your name refers to you, specifically and concretely, it does not refer to the concept of "person" or "people."
But to take this further, imagine the following thought experiment:
You have a newborn infant, and you isolate them from the rest of the world (remember this is a thought experiment, so we are not bound by ethical considerations for this purpose). You show them 3 identical staplers. You call the first one "Foo", the second one "Bar" and the 3rd one "Baz."
An infant might, on their own as they grow and mature, start to abstract and conceptualize a concept of a logical grouping here. They might observe that Foo, Bar and Baz have similarities and, being humans, they might even come up with some kind of verbal or non-verbal cue to reference this abstract concept.
But for a while at least, these are individual concretes. If all they ever see is one single concrete "stapler", they may learn to associate the word with the concrete and never even think about abstracting it. But if they do start to abstract it upon observation of similar "things" ... to what degree are non-humans capable of doing that?
You provide a lot of good evidence that dogs can to some degree. But to what extent? What are the limitations?
These are unanswered questions in both science and philosophy.
I hope I answered your question, as it was a valid one. I'm not giving answers to these hypotheses and philosophical conjectures. I'm saying that this is something that is still not quite figured out yet.