If he's an older dog, he's probably used to his name; however, changing it isn't out of the question. If he's from a shelter, they may neglect to tell you that he has a temporary name assigned to him by staff. If he's from a breeder, he'll come to you with a long name, which you may want to shorten, or change. And if he's coming out of an abusive situation, a new name may represent a fresh start. But we're lucky: dogs are extremely adaptable. And soon enough, if you use it consistently, he will respond to his new name.
Submissive urination is a normal way for your puppy to demonstrate submissive behavior. Even a dog that is otherwise housetrained may leave dribbles and puddles of urine at your feet when greeting you. Excitement urination with a puppy is usually caused by lack of bladder control. The puppy is not aware that he is urinating; he's just excited and any punishment will only confuse him.