First, make sure your puppy is comfortable wearing a leash. This can feel strange at first, and some puppies may bite the leash. Give your puppy treats as you put the leash on each time. Then, stand next to your puppy with the leash in a loose loop and give him several treats in a row for standing or sitting next to your leg. Take one step forward and encourage him to follow by giving another treat as he catches up.
Help him relax when he comes home. When your puppy gets home, give him a warm hot water bottle and put a ticking clock near his sleeping area. This imitates the heat and heartbeat of his litter mates and will soothe him in his new environment. This may be even more important for a new dog from a busy, loud shelter who's had a rough time early on. Whatever you can do to help him get comfortable in his new home will be good for both of you.
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.
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.