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.
Always remember that you are dealing with a very immature young animal. Be realistic, flexible, patient and always fair during puppy training sessions. Your puppy doesn't just automatically know this stuff! It's all new to him and he is bound to have the odd slip up and mistake along the way. Don't worry about these mistakes, just move on and do your best to prevent them in the future.
Remember that training is an ongoing process. You will never be completely finished. It is important to keep working on obedience training throughout the life of your dog. People who learn a language at a young age but stop speaking that language may forget much of it as they grow older. The same goes for your dog: use it or lose it. Running through even the most basic tricks and commands will help them stay fresh in your dog's mind. Plus, it's a great way to spend time with your dog.
Imagine your puppy running out the front door. You call him, waving a treat. But he'd rather chase a squirrel into the road than come back to munch on a treat. In addition to the obvious danger of Puppy getting hit by a car, he learns that he doesn't have to listen to you. He learns that he's in charge of what he decides to do and what he decides not to do.