Given that our assumption that other humans brain’s work in a similar way to ours seems to be quite wrong,
Eh, maybe not.
Having done some quick reading, and speaking with my resident biologist... we should not equate our conscious experience with the fullness of our thought process, most of which happens without our being aware of them. People using inner monologues, and those not using such, don't so much "think differently" - they present their thoughts to themselves differently.
Basically, the inner monologue is a kind of user interface to your thoughts. It is the words on the computer screen of your mind, but you only see the results, not the data processing going on in the CPU.
If I want my cats to come, I call them by name, even though the concept of “name” is incomprehensible to them.
So, that one I know a bit about. Animals do not possess language, and they don't have an
abstract concept of names, in general.
However, dogs and cats do associate sounds with things. The can opener is associated with "tuna will be available", and so that sound
means the thing. Their understand that the noise of their name is a reference to their self.
Moreover, they get that the noise of their name is different from the noise that demands an action. If you have two pets, they know the difference between "Jimmy, come here" and "Sally, come here". Sally can figure out that she doesn't need to show up when you call for Jimmy.
I don’t think it makes a difference when the images are formed. It is still using the brain’s capacity to create a picture of things that do not exist.
Yes, but the brain's ability to make a picture, or even to have a picture associated with some emotion, is different from
building a narrative of pictures, which is what we are usually talking about when we speak of dreams.
However, how would sleepwalking and other parasomnias work if that where true?
Well, parasomnias typically happen during non-REM sleep, when we
are NOT dreaming, so dream processes won't tell us much there.