Your dog will have a special affection for you and be loyal to you, but they will not see you as their “owner”. This is because they do not have a concept of ownership. Ownership is a human concept which relates to capitalism. Your dog does not know that you have exchanged money with another human in order to own them. Your dog only knows that you love them and care for them like a parent.
This is one of the many reasons why adopting is a much better idea. With an adopted dog, you won’t be their owner and your dog will know that you have rescued them. Humans don’t own their dogs any more than they own their children. You are simply their friend and caretaker. You are as much your dog’s human as they are your dog.