Do you mean as in the last name is also a first name or do you mean a double name? I'm not sure what it's called when your last name is also a first name. I don't know that it would even have a name, really because what does that actually MEAN? Surnames are becoming first names all the time, and people had first names long before surnames were invented, so I just don't know.
On the other hand, if you mean they literally have to first names (for example, I know a girl whose first name is Geri Ann, with a space in the middle -- it is not (fn) Geri (mn) Ann), I have always seen them referred to as double names. Sometimes they are hyphenated and occassionally even just smushed together (ex, my best friend LeeAnne, named for her father Lee and her aunt Anne, though I realize when you get into those -ann names they might not actually be such good examples ).
I'd be interested to see if there is a word for having a last name that is also a first name, as I have that. My last name is Luther, which has caused a lot of funny problems when I was a teacher> Way too many of my students had never heard of Martin Luther (even at the parochial school!), and always thought it was funny to ask if I was related to Martin Luther King. I would usually look at them blankly and say "No, my last name isn't King", and you'd always have some yahoo in the back who thought he was incredibly witty gasp out "and you're not black!". Of course, then I'd always turn it into a boring history lesson by explaining how Martin Luther King got his name and who Martin Luther was. heh heh heh Don't mess with Mrs. Luther when it comes to names!! LOL