When I go to Hamburger -> Anime, or Hamburger -> TV shows, it has the same style of semi-logical groupings of categories as I see normally: Crime shows, action shows, classic shows, suggestions for me, etc -- but there seems to be no affordances to affect ordering, nor menu items that would reflect that. The settings menu is useless, as it consists only of links to the account details, privacy statement, and terms of use.
I really hope that the answer isn't "Log into our website instead of using our native app!", though perhaps the feature warrants such an experiment.
In the Android mobile app, which has recently seen some excellent improvements, I'm unable to find an alphabetical listing as well. One can select genres, and TV shows vs movies, but there are no affordances for sorting, only a wall of categories to scroll through.
The home page is for discovery based on your past preferences/popularity. And there are TV and movie pages in which you can display shows by genre or even A-Z.
Disclosure: I work at Netflix and would like to make it better for everyone who uses it.