Any apostrophe rule would also have to apply to plural possessive, as well as nouns (and names) ending in "s". Unfortunately, "the dogs's kennels" looks a bit excessive, and "the fairly floss's colour" is falling into bizarreness. Too many S's! (S'??) So maybe we're fine with a tacked-on apostrophe and no extra "s". I believe that's the general rule... Though Andrew does have a point, we *are* saying "James-es". So my counter-question is, should it apply to a "z" ending also? "Jazz's story" or "jazz' story"? Happy to theorise. ^^

I think the correct form is James'. As far as I know there is a rule about these nouns, although I can't remember it exactly, but this is how I form the genitive form of nouns ending in "s"

Maybe just "jazz story"? "Jazz" being not a possessive form, but a modifier?

In this case, I would write "james's dog", pronounced as jameses, where the apostrophe-s is denoting ownership. A.