One of my college classmates had the surname Morris, and married another Morris. I occasionally see Ms. Morris Morris (as her name appears) mentioned in alumni news updates.
My last name is Irish, but gets butchered so much you’d think it were German. 
It’s all of four letters, two syllables, and one consonant, and the variations people come up with are endless. The “unique” thing that Sarahfeena mentioned is the only benefit to having this name, and getting rid of it is one of the main reasons I’m willing to get married someday. And my SO’s last name is great: easy to pronounce and spell, not easy to turn into a taunt, clearly a surname, and it’s Italian (which is the other part of my heritage).
Here’s a fairly prominent woman (Ted Kennedy’s campaign manager in New Hampshire, once) who married a man with the same name as her…
Of course, it was his LAST name that was the same as her first name. Hence, she ended up with the unenviable name Dudley Dudley.
Mine was phonetic, too, but it was four syllables and ten letters, and completely unfamiliar. I don’t really blame people for not getting it; I’m also really bad at sounding things out for some reason.
My paternal grandmother had the same name as my paternal grandfather. I was told that it was a very common name in the area of Russia where they lived, although it’s extremely uncommon in the U.S. (It is Kritchevsky) They did have trouble when the arrived at Ellis island as the intake person didn’t think they understood the questions when they asked her maiden name. They didn’t speak English well enough to communicate that they understood, it’s just that her married name was the same as her maiden name.
My grandparents finally gave her a different spelling for her maiden name - which satisfied the intake person and allowed them to proceed through immigration.
We don’t have a marriage name problem – Pepper Mill kept her last name.
I’ve known two other couples who did that.
I was ready to ditch my maiden name* anyways so it didn’t provide a problem for us. I did consider changing my surname to Cheez_Whia’s (my mom, for those not in the know) maiden name before I got married, though. The timing worked out though that it was easier to take my husband’s.
*Since we’re on German surnames: my maiden name was German, 4 letters long, with one vowel (no diacriticals) and one syllable. It is only one letter off from an extremely common English noun. People CONSTANTLY misspelled and mispronounced the damn thing. At least with my new WASP name I just get people leaving off the terminal “s”.
I once knew a Smith who married a Smith. She still had to go through nearly as much paperwork as if she’d changed her name, just to change her status to “married” on a lot of documents.
Except for the ones translated by yours truly, TYVM. 
When I was in Spain in 2002 I stayed with a family where both sides were Rodríguez, so the Mrs. was Celia Rodríguez de Rodríguez and the son was Javier Rodríguez Rodríguez.
I knew an unmarried couple (they’ve since broken up) that had the same last name, which was uncommon enough that those two are the only ones I’ve ever met or heard of with that name. Complete coincidence, or so they tell me.
I changed my last name both times I was married.
I changed my German maiden name that was butchered to a Polish name that was butchered to an Irish name that is butchered.
With my maiden they left out the ‘n’, in the second they inserted an ‘n’ that was not there. With my name now they leave out the first ‘L’ and insert an ‘h’.
I guess I could bite the bullet and change my name to my bio dads last name. In this case it would get pronounced correctly but I am sure it would be spelled wrong as there is a "u’ in there that makes it uncommon to the most popular way to spell it.
My aunt lived with a man with the same surname for a while and they ended up having to get a divorce to terminate what had become, somewhat legally on some documents, effectively a common law marriage.
A college friend married a woman who already shared his surname.