Many iterations ago, my WIP started with an unnamed set of characters, one who discovers a killing and another who arrives looking for the killer. I didn't include their names, because, I thought, it wasn't important. The reader didn't need that information, not so early in the story. My reader would be more engaged if I didn't give the characters names, right away.
I was wrong. Their names were important, extremely important. Not naming them served absolutely no purpose in my story. It did not further the plot or the mystery. It was not integral to the setting (I haven't written any dystopia lit). These were characters, not disembodied, faceless "storytellers." In fact, several readers had a hard time keeping the two characters straight - one woman, the other a man. How hard was that? I thought.
Turns out, very.
After reading hundreds of MG and YA novels across genres, I've seen some excellent examples of authors using unnamed characters (dystopian, where not having a name is part and parcel of society) and unnamed and unreliable narrators (think crime, mystery and spy novels). So not naming a character can be integral to your story, if it's done consciously and to further the story.
This is an excellent article about adult literary authors eschewing character names for numbers, assumed names, or less. In most cases, not naming the character was integral to the setting, the plot, or the genre. Or, as in Heart of Darkness, Conrad purposefully distances the reader from the storyteller, and the story telling, by never naming the narrator.
Recently, a colleague admitted she'd done the same thing I had - not named a key character in her story. She waited a couple of chapters to introduce names, because she didn't think the reader needed to know them right away. When she rewrote it and included the names in the first few pages, she received some really great feedback. That's when I realized that starting with an "unnamed character/s" is probably a fairly common beginning author mistake.
Our characters' literary lives are short - 300 pages or so. Name them, up front and quickly, to avoid confusion but also to pull your reader into their worlds. It's hard to care about a character who has no name.
As for an example of unreliable narrators, the best I've read is the first half of this wonderful book. Be prepared to cry your eyes out.