While there is no obligation to have an official Jewish name, it is definitely something a Jewish person should have. Choosing a name should be easy. Here are some suggestions for choosing a name. If your name is an anglicized version of a Biblical name, choose the Biblical version. If you are named after a relative, find out what that person's Hebrew name was. (If this relative is no longer alive, it is possible to look for the name that appears on the grave or on the Ketubah – marriage contract.) If neither option applies, just choose a Jewish name that either sounds similar to you given name, or begins with the same letter.
Whatever name you choose, enjoy it!