I know I've heard of word that is used to describe when someone has a last name that could easily double as a first name.  ie: Joe Paul. I cannot remember the word.  Do you?
Welcome to the forum rchapman. Tough question. Some discussion here but no real consensus.
Browsing there and elsewhere, I found the following "answers" ...
- unconventional anthroponym
- reversible name
- surname name
- There is no special word describing this, since parents can name their children anything they want, so it's simply a name.
Sorry I couldn't be of more assistance. Maybe some other forum member will have an idea.
I saw it in one of the daily word calendars years ago.  The last comment is irritating though...of course parents can name their kids anything they want.  That doesn't preclude their being a name for this circumstance.  It's not very common. Thank you for trying:) Â
No problem. If you do ever stumble across the word you're looking for, please share it here. Thanks.
Surnames haven't been around all that long. I've been told, but have never had it verified, that the King )perhaps of England?) demanded that families adopt a surname and strong advice was that it be an occupation (Joe Don Baker) or a color (Giuseppe Verdi, whose name translates as Joe Green) but many people adopted a surname indicating where they came from geographically or genetically(Catherine of Aragon, Ponce de Leon).
Nikita Khruschev was called Nikita Sergevich, (son of Serge) and his kids would be called Nikitavitch as well as Khruschev. It's not so much that parents are allowed to give their kids and given name (Moon Unit Zappa!) but a significant fraction of all people change their surnames, and not just women. Gerry Ford was originally Leslie King, and Bill Clinton was William Jefferson Blyth III. I recently posted of Bo Diddley and Jelly Roll Morton.
Native Americans commonly adopted different names at different stages of life, which makes sense; you're not the same guy you were when you were decades earlier.
But I'll pose a question that's related. Your last name is a patronymic, or a surname. Your first name ought not be called your Christian name if you are Jewish, and "given name" is, like "first name", pretty wordy. Can you think of a one-word synonym?