Why would Filch from Harry Potter 2 say: “… go now, I have to write up Peeves’ report … go …”
Would saying Peeves’s have been a mistake?
Whether to write (or enunciate, in speech) that second (possessive) s after a subject noun that already ends with s is a stylistic choice. But the orthography should always reflect how you would pronounce it (if you had to actually read out your text, say).
It's the same with, say, Charles's wife, Jesus' life. But note that to some extent writers/speakers may make different choices depending on exactly how easy they find it to articulate the repeated consonant with the specific noun (i.e. - any given person might not make consistent choices).
But I venture to suggest that if we postulate a context where there are already many instances of the potentially troublesome sibilant phoneme, such as a man with two "high maintenance" mistresses...
My mistresses's dresses are costing me a fortune!
...no-one would actually write (or attempt to articulate) the final Saxon Genitive s unless they were being deliberately facetious.
The possessive form of a singular nouns ending with the letter s can be either:
The noun with a following apostrophe: Peeves' report.
The noun followed by an apostrophe and another letter s: Peeves's report.
Either is correct and the choice is a matter of style.