Think of it as this: The first name is your personal identifier and the last name is the name you get from your family.
See how mine is Magnus Tarmon? Magnus is the name that people use to identify my character and Tarmon is the name that makes him part of the Tarmon family.
My favorite is still the guy called *** Cancer that was forced to change his name, which is all the more funny when you consider that a great deal of XIV itself is written like SE just realized that sex is a thing that exists anyway.