The answer to the riddle, "What belongs to you, but others use it more than you do?" is your name. This is example of just one common riddle that revolves around names.
Another classic name riddle asks, "What is so fragile even saying its name can break it?" The answer is silence. The answer to the riddle that goes, "How could a cowboy ride into town on Friday, stay two days and ride out on Friday?" is that the horse's name is "Friday." A nautical name riddle wonders, "This runs fore to aft on one side of a ship, and aft to fore on the other. What is it?" Anyone who can follow those descriptions realizes the correct response is the name of the ship.