The Unveiling of My New Word(s)

Is there a name for the occurence of when a person has a first and last name that are the same, like Jordan Jordan or Carter Carter? And I wonder, are there very many people whose parents blessed them with such a combination of names? And of those people, how many have taken the effort to legally or informally change them? If there would be a designated word for such treacherous namesakism, I would call it synaname.