Under any name, King mesmerizes the reader.
I didn't find the phrase in my dictionary. What does it mean in the sentence?
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Hard to say without context, but it's probably literal. Some authors use a pseudonym, i.e. a fake name. If it's talking about Stephen King, he published some of his books under the pseudonym "Richard Bachman". So the writer here is saying that whatever name the author uses, whether "Stephen King" or "Richard Bachman" (or if he's talking about some other writer named King, whatever names that writer uses), he still "mesmerizes the reader".