Brevity is the soul of wit. Sometimes people want to keep names short and simple. There is no need to have a shortened nickname when your name is three letters long.
Since 1950 the names Joe, Roy, Jon, Ian, and Eli have claimed the #1 spot at different points. For girls the #1 names are made up of Ann, Kim, Amy, Zoe, Mia, and Ava.
If you don't like these name maybe you'll find more suitable names among the most popular names that are ten letters or longer. You can also see the animated geographic history of short names in America here.