Well, famously, the main character/narrator in REBECCA is never named or identified… except after she marries Maxim de Winter and becomes “Mrs de Winter”, which doesn’t quite count.
I can’t think of any movies off the top of my head, but if I can stretch the rules a bit to include TV, there’s always The Prisoner. The real name of Number 6 is never given, probably because it’s completely irrelevant. Symbolically he’s an everyman (wasn’t that even the name of McGoohan’s production company?), so his name doesn’t matter, despite some fans’ assumptions that the character was supposed to be John Drake from Danger Man.
Purple Rain - Prince is only refered to as The Kid.
Both Arnold Schwarzenegger’s character and that other guy have serial numbers in that movie. T-2000 & T-3000 or somesuch.
And E.T.'s name is E.T. That’s what the kids call him, and that’s what he ends up calling himself.
Yes. Wally. I think Andre used it.
There’s also “The Monster” (Frankenstein) and “The Doctor” (any of the various Drs Who.
I think the other guy in My Dinner with Andre is just supposed to be Wallace Shawn.
Yeah, but nobody calls them that. Just because I have a Social Security number or a Driver’s License number doesn’t mean it’s my name.
The Bride’s name is used many times by Bill himself in Vol 1, unbeeped.
The main character in Bad Lieutenant is unnamed. IMdB lists the character as “The Lieutenant”, but I’m pretty sure that the closing credits list him as “LT”.
The Thing.
The “I” of Withnail and I was called Marwood, but wasn’t identified as such in the film.
In Jesus’ Son, Billy Crudup’s character is often referred to as Fuckhead, but obviously, that’s just an epithet. He’s listed in the credits as FH and is never given a formal name. Does that count?
I’m not sure that it counts, if the character is called by a consistent nickname by the other characters. For instance, folks regularly address E.T. by that name, and he responds. If we’re going to count nicknames or pseudonyms as “no name”, then there’s a plethora of examples of this phenomenon (was the Sundance Kid ever named, for instance?). On the other hand, to use the OP’s example of Waterworld, nobody says “Hey, Mariner”. Nobody addresses him by any name at all, so “The Mariner” isn’t a name, or even a nickname, but merely a description.
But see, that’s just the thing though… I don’t specifically remember many, if any, calling him that but it being more implied (??) by other characters as a description of his uselessness. I don’t know, it’s been a while since I’ve seen it and thought maybe it would apply since the closest he comes to having a name listed is just the “FH.” So, once more, I’m clueless. Anyone else seen this who might be able to shed some light on it?
Uh, actually the Hulk’s name is Bruce Banner. He’s still the same person, so I don’t think he loses his name when he get’s big and green.
There really was a Sundance Kid - he’s not fictional, merely fictionalized (aren’t we all?). His name was Harry A. Longabaugh, but “Sundance Kid” is of course way more memorable.
/The Kalmar Kid
I believe he’s called “Joe” by the owner of the hotel, or by somebody else, in A Fistfull of Dollars. Whether Monco is his real name sorta depends on wether or not you want to beleive it is a trilogy. I’ve read in quite a few places that A Fistfull of Dollars was supposed to be a stand along movie, and not a prequal to For A Few Dollars more. However it fits in so well, and Eastwood is so much like his previous character in AFFoD that most people just automatticaly consider it a sequal. Leone meant for AFFoD to be a stand alone flick, but popular opinion turned all three movies into a trilogy.
So, if it’s a trilogy, then we can all assume he has no name, but has a nickname in each movie so that the audience can label him with something, but no actual name or history so The Man With No Name grows in the imagination of everyone that watches the movies. He is called Monco by a sheriff in For a Few Dollars More, but it’s just easy to assume the guy created a nickname for himself, rather than giving out his real name (IMHO anyways) considering the enemies he made in the previous movie, or in his past.
If you believe AFFoD is a stand alone flick, then it’s reasonable to beleive Monco is his real name. But in that case, why isn’t he called that more than once throught FaFDM and TGTH&TU?
Not only that, but his name was mentioned a few times in the movie. Regardless, I’m sure Chronos is aware the Sundance Kid was a real person with a real name. It seems to me his point is that “Sundance Kid” counts as a name because people call him that regularly and he responds to it.
Uh…because I believe AFFoD is a stand alone flick. 
Sergio Leone never meant for it to be a trilogy. FaFDM was intended to be a sequel to AFFoD and he was simply given a name, Monco, in the 2nd one. I don’t ever recall him being referred to as Joe in AFFoD. (I have an old book about this where Leone is interviewed about the whole “trilogy” thing, I can look it up later).
It’s pretty clear that’s he’s Blondie in TGTB&TU. Everyone knows him by that name, and it appears that he has a history with both men. Plus, Lee Van Cleef isn’t playing the same character, so why should Clint? Van Cleef wasn’t even evil in the 2nd one.
I think Clint’s character in Pale Rider qualifies. They call him Preacher, but that isn’t really his name.