Clint Eastwood’s ‘Man with No Name’ seems like the obvious one, as DrDeth pointed out. But he needs a name, so I choose to call him… Tim.
Buford “Mad Dog” Tannen: What kinda stupid name is that?!
The Dain Curse, a novel by Dashiell Hammett featuring the unnamed Continental Op. When turned into a TV miniseries in 1978, the Op was given the name “Hamilton Nash.”
Interesting. I didn’t know about that one.
It always bothered me that Hammett never named The Continental Op. You could argue that the whole point was that he was anonymous, but in my case, the title “Continental Op” gave me a completely erroneous image of what the character was supposed to be, before I got hold of and read the stories.
I just thought of a non-literary one:
The video game Doom (id Software, 1993) has an unnamed protagonist (known as “Doom Guy”).
For the film adaptation in 2005, they named the main character, played by Karl Urban, John “The Reaper” Grimm.
Clint Eastwood’s character in High Plains Drifter does not have name either. He’s credited as" The Stranger".
EDIT: I just remembered Eastwood"s character in Pale Rider is credited as “The Preacher”.
Warning: Lame Game of Thrones Joke ahead:
Wasn’t “The Stranger” part of the Magnificent Seven?
Well yeah, every character is going to be an action figure and you can’t trademark ‘walk on #3’.
Let’s not forget the bass player from That Thing You Do!, who goes unnamed during the movie and is impishly identified in the credits only as … T.B. Player.
They’re both the same character. 
The character he plays in HPD is Jim Duncan, (deceased).
Wells did give The Invisible Man a last name, Griffin. But no first name, which had to be invented for subsequent adaptations.
In the 1933 movie (with Claude Rains) the character was Jack Griffin.
In The Invisible Man Returns (1940) the original invisible man was named John Griffin.
In The Invisible Man’s Revenge (1944) the character’s name is Robert Griffin.
A Russian 1984 adaptation used the name Jonathan Griffin.
In the original Hollow Man the protagonist was named Sebastian Caine. But in the sequel, Hollow Man 2, the protagonist was a new character named Michael Griffin.
In Alan Moore’s comic book series, The League of Extraordinary Gentlemen, the character is named Hawley Griffin.
In Jeff Lemire’s comic book, The Nobody, the character is named John Griffen.
And some adaptations changed the character’s last name. The 1958 British TV series, The Invisible Man, named the character Peter Brady, the 1975 American series used Daniel Westin, and the 2000 series used Darien Fawkes. The 2005 cartoon series named the character Alan Crystal. The 1992 movie, Memoirs of an Invisible Man with Chevy Chase, used the name Nick Halloway.
He similarly didn’t give Dr. Moreau a first name.
In the second volume of The League of Extraordinary Gentleman, Alan Moore named him Alphonse Moreau
The 1932 movie Island of Lost Souls doesn’t give him a first name. Nor does the 1996 movie with Marlon Brando.
In the 1977 movie Burt Lancaster was Paul Moreau
He’s shown up in a number of sequels and pastiches, but I don’t know of any other that name him.
When I was at the University of Rochester, future Nobel Laureate Gerard Mourou had an office down the hall. Every time I’d pass it, I involuntarily though “The Office of Dr. Mourou”. So I sorta think his first name should be Gerard.
Also, Kenner tended to give many of the figures generic names like “Hammerhead” and “Walrusman” when the characters were later used in the extended universe era of Star Wars licenced material, they were usually given different, more “Star Warsish” names like Momaw Nadon and Ponda Baba.
Conan Doyle never gave a first name to Insp. Lestrade, Sherlock Holmes’s frenemy at Scotland Yard, just a first initial, G., mentioned in a single story. I always thought his first name was probably that quintessential 19th C. British name, George.
We’re not even sure what Watson’s middle name is. The initial is H.
In “Burnt Offerings”, I’d like to name the smiley hearse driver Wink Martindale.
Or Sunshine.
In “Animal Hose”, Belushi smashes a guitar played by a proto-hippy who probably should have been named Chad.
It’s been fanwanked that his middle name must be Hamish. Because while Conan Doyle rarely mentioned his first name, he had said it was John. But then in one of his later books, he had Watson’s wife call him James. To explain this within the story, some people have said that Mary Watson must call her husband by his middle name, which must therefore be Hamish, the Scottish version of James.
This is nonsense. Everyone knows that Watson’s middle name is Hiberius.
In the recent ‘Sherlock’ series, his name is Greg.
In a satirical play I wrote, I combined the two Scotland Yard detectives from the Holmes stories, Gregson and G. Lestrade, into “Gregson Lestrade”.
There was a series of novels focusing on Lestrade that came out in the early Eighties IIRC, in which his first name was given as Sholto (the last name of the brothers in The Sign of Four). Don’t know why the author would’ve ignored the data point Conan Doyle supplied.
Animal Hose was a bestiality porn movie that came out a few years later, wasn’t it?