Even if your name is seemingly uncommon, like "Seymour Mazlow Freen", there's always a chance that there might be at least one other person out there with an identical name, so banks and other institutions usually rely on unique identifiers, like a Social Security Number. Having a very common name can sometimes be difficult; try checking into a hotel when your real name is "John Smith" and see if you don't get a sly look from the desk clerk.

There actually is a "Jim Smith" club in the US whose members are all men named Jim Smith. Obviously, when they attend their annual convention they can't address one another as "Jim", since 400+ people will answer! So they instead put their home towns on their name tags and are known as "Jim Detroit" or "Jim Miami."
Then there are parents who can't resist having fun naming their new baby something comical when they have a surname that lends itself to such possibilities. For example, I once read about a local man whose surname was "Duck" and his parents named him "Donald." His problem was that almost 50 percent of the time when he tried to make a reservation somewhere or order something over the telephone, the other party thought it was a prank call and hung up on him.
Technically in the US, a parent can choose any surname at all for their child when filling out the birth certificate. So even if the mother's surname is "Jones" and the father's is "Brown," they can choose to name their child "John Miller." Not many people take advantage of this option, however, and it is customary for the child to take the father's surname. Sometimes single mothers will use their surname for the baby and not the father's. If the mother gets married later, she can apply to have the child's name legally changed. In fact, an adult in the US can also apply to legally change either his first or last name (or both), as long as they are not doing so for fraudulant purposes (for example, if they are criminals and want to change their name to avoid capture).