In the movie Maanagaram (2017), most of the main characters don't have names.
Is there a name for this genre of movies in which the main characters don't have names?
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As Nuclear noted in the comments, the idea of never naming your main character(s) is more of an aesthetic choice - a detail. The best term to use, I think, would be to call it a trope. In fact, TV Tropes calls this the "No Name Given" trope.
(Standard disclaimer regarding people having lost hours of their lives to the TV Tropes website. It's like the Bermuda Triangle of the internet.)
There's no genre name for this, because it isn't really a genre. Mirriam-Webster defines genre thusly:
Definition of genre
1: a category of artistic, musical, or literary composition characterized by a particular style, form, or content
2: kind, sort
3: painting that depicts scenes or events from everyday life usually realistically
Of which, the first definition is what applies to movies. So, a genre is a category of film; it describes, in broad strokes, the general atmosphere, emotional expectations and plot progression one can expect when watching the film. It doesn't really describe specific details (or lack thereof) in the film.
For example: Horror. If you're going to watch a horror film, you can expect it to be scary. You can expect it to be dark and possibly gory, generally unsuitable for children. However, you don't necessarily know exactly what the monster/killer/whatever will be. (Unless it's a sequel to a long running franchise, or the name of the movie somehow gives it away, but these things are outside the scope of "genre.") You can't tell what the characters' names will be based on the genre.