While it may not be very common, as suggested or explained in previous answers, the answer is actually,
In example, some science fiction works explore human identity through the construct of "Doppelgangers", in which some doppelgangers exist in the form of characters with the same name and similar appearances, but they come from either other timelines or universes.
Fringe, The Man in the High Castle, and Counterpart are all stories about parallel universes, in which counterparts have the same name, and despite some visual differences, characters pretend to be their counterparts as an infiltration tactic.
There are also other cases in science fiction where either temporal phenomenon occur or their is time travel present, characters may come across known characters (with the same names), but at different ages.
LOST and the upcoming TV series adaption of The Time Traveler's Wife are examples where this happens, but in TTW's case, there are times were the characters are similar enough in age that the audience may have to guess when it is, but this is all about the idea of exploring identity in a more intimate way, or to ask if identity is fixed or fluid. Can human identity truly be defined as we age?
Sometimes fantasy, such as Game of Thrones, will also use doppelgangers via magic, to make themselves appear like other characters and assume an identity. The mythology behind The Faceless Men would be a specific example, as the *TV audience only knows the name "Jaqen H'gar", where in the book their is distinction between two men sharing the same face & personality: H'gar and The Kindly Man. There might be a mythological debate about identity when someone wears the same face and believes in the same things, if anything actually makes them different person? These seems to be the idea behind The Faceless Men. IMO the TV series adaptation made this more ambiguous with how they used both H'gar and The Waif in attempting to condition Arya.
Once in a while, it might be used as a kind of running joke. I can not think of a TV series that has done this (although I think another answer has), but the fantasy-adventure dramedy romance film series, Pirates of the Caribbean has a running gag of the surname name "Smith" or "Smyth". (You can see my answer to see the list I made on another Q). This also then would make the recurring surname "thematic" to POTC series. However this not integral to the plot or there is nothing on screen that would make all the Smiths confusing. It's just a small amusing thing.