A literary example is Edgar Allen Poe’s short story William Wilson. It was adapted to film, most notably in the 1968 anthology Spirits of the Dead.
I was swimming in the ocean of tvtropes.org just now, and accidentally discovered that they have a page that lists tons of examples of stories with two or more characters of the same name:
And a non-literary example is the two Willie Wilsons who played major league baseball in the 1980s–both were black, speedy centerfielders without much power, but other than that, they wouldn’t have been mixed up much. One of them actually went by “Mookie” so there was no real confusion.
That reminds me that the Mets at one point had two pitchers on their roster named Bobby Jones. Their jerseys both actually had the names “Bobby Jones” on them, differentiated by their middle initial.
Which resulted a brief period when only two of the four major American sports were Mookie-less.
The Sopranos also had two characters named “Pussy.” “Big Pussy” was one of Tony’s crew, and “Little Pussy” was Junior’s rival he intended to whack at Artie’s in Season One.
I worked at a place where we had “Jennifer One”, “Jennifer Two” and “Jennifer Three” (numbered in the order in which they started working there).
We had three Jennifers on my dorm floor in freshman year. One went by Jennifer, one went by Jenn, one went by Jenny. No confusion.
In The Hitch-Hiker’s Guide to the Galaxy, some shared names were offstage. Zaphod Beeblebrox’s father was Zaphod Beeblebrox the second, his father was Zaphod Beeblebrox the third… And then there was Arthur Philip Dent, called a jerk and an asshole by Wowbagger the Infintely Prolonged, the latter of which then planned to move on to insult a slug of the species “Arthur Philip Denu” (I know there are a bunch of hyphens in that but I don’t have the book handy here at work). Fun joke, but one that makes no sense even by Adams’ standards. Babel Fish or not, WtIP is still working his way through English-language Christian names.
These are the Daves I know, I know
These are the Daves I know.
Some of them are Davids, But most of us are Daves.
They all have their own hands, but they come from different mums.
In the ‘70s, there was Quark, a Mel Brooks outer space comedy starring Richard Benjamin. One of the crewmen was Betty. She had a clone also named Betty. No one was sure which was the real Betty. Collectively, they were The Bettys (played by the luscious Barnstable twins).
Wikipedia says Buck Henry created:
Brian
(vaguely remembers watching the show)
Come over here. ::whispers:: Buck Henry and Mel Brooks are the same person! I know, right! 
Funny, I thought Quark was a garbage man but then I was getting confused with Salvage One and Andy Griffith. Trust your first instincts (except Mel Brooks/Buck Henry).
He was. He was the commander of a “United Galaxy Sanitation Patrol Cruiser,” dispatched to collect space garbage.
Andy Griffith’s character in Salvage 1 was a scrap dealer and junkpicker.
The Batman mythos has a Harvey Dent and a Harvey Bullock
At least you ran out before you got to Jennifer 8.
The slug doesn’t have an English-language Christian name. It’s not Babelfish; it’s Library of Babel. The Universe is so big that every string of characters spells the name of some insultable creature or another, and the slug only looks like it has a Christian name because it’s right after another character with a Christian name.
And one of my classes right now contains three Elizabeths and an Elyse. Fortunately, one of the Elizabeths goes by Eliza and one goes by Lizzy, so it’s easy to distinguish them. The same class has a Clair and a Claire, who are apparently close friends and don’t mind being called each other.
I know it’s not the same thing but there are a lot of shared names in John Ford’s cavalry trilogy. There are similarities of theme and setting but I they are different characters even though the names are the same or similar. I’ve never found an answer as to why he did that.
Rewatching some episodes of Arrested Development, and there’s the two Lucilles.
And a loose seal.
The comic strip Peanuts had two distinct characters named Patty.
The first was the character some fans have named “original Patty”, a blonde girl who was a regular in the early strips, and was in the very first strip, but never developed any particular memorable character traits. She basically just disappeared without any explanation that I saw.
Then came “Peppermint” Patty, a redhead with a much more interesting personality.