Can anyone explain to me why several book review sites are called "what I have been reading" when they describe books the reviewer has read? why aren't they called "what I have read"?
You've tagged the question present-perfect and present-perfect-progressive so I assume you know the definitions.
"what I have been reading"
This is present perfect continuous or progressive and suggests that something is unfinished.
"what I have read"?
This is the present perfect simple and indicates an activity that has finished.
In your example
For book reviews, the use of present perfect continuous (I have been reading), will indicate "recently read books". This technically means "The book that I have been reading in the last few days and have not finished". However, this opinion can be project to last week. Today I have finished a book but last week I was still reading it, so it does still qualify as a book that "I have been reading" if spoken about from the time when I had not finished it. Hence recently read books.
For book reviews, the use of present perfect simple (I have read), would say span your lifetime. For example, the best urban fantasy book that I ever read. The best series that I read (could have been 30 years ago).
Now in this context, this is fairly flexible, there is no cut off time per say. For example I could say "books that I was reading as a teenager", imagining myself back there. Or I could say "Books that I read as a teenager", speaking from today and looking back. But generally speaking "have read" indicates a finality, in the past and long finished, but "have been reading" indicates unfinished, implying recent past.