Fantasy writers love apostrophes in names. They have done so at least since the pulps of the 1930s, although their use was probably popularized by Anne McCaffrey’s Pern series. On Pern, a person’s name is shortened when they become a dragon-rider, so the series includes characters with names like F’lar and F’nor. It seems an unlikely custom to me, but at least McCaffrey uses apostrophes in an immediately recognized way. By contrast, the only answers I have coaxed from imitators is “it’s cool” — never a good reason for background details — or that the apostrophe indicates a pause — which is not a standard reason for using an apostrophe. Few have any idea why the apostrophe is there.
In English and French, an apostrophe indicates that some letters are left out. For instance, in French, “d’Erlon” is short for “de Erlon,” and reflects the oral habit of dropping a duplicated sound. In English, an apostrophe by extension indicates possession, because in Old English, the possessive ending was “es” and Modern English does not pronounce the “e.” In addition, an apostrophe is used in attempts to render non-European pronunciations using Latin characters. For instance, in the Haida language of the Pacific Northwest l and l’ are separate sounds. So are k and k’. However, only experts in a given language can be expected to know the conventions, so if you do decide on an unorthodox use, at the very least you should provide a pronunciation guide at the start of the book. If you don’t, you risk readers settling on an embarrassingly inappropriate one, as Ursula Le Guin found out when she learned that her wizard Ged from A Wizard of Earthsea was called Jed by some of her readers, making him sound like a hillbilly from an 1960s TV show..
On the whole, though, it’s best to stick to the standard English purposes when writing for an English-speaking audience. Mysterious apostrophes are almost always an exotica too far, like names without vowels or ones full of Qs and Xs. Many readers will simply substitute a blank in their mind for a name that is too exotic, which estranges them from the story, especially when several names are replaced by blanks. If you must use exotic punctuation, accents and diacriticals are available from your keyboard and are easy to look up.
Apostrophes in fantasy names are a rookie’s mistake, and make the writer appear illiterate. In A Tough Guide to Fantasyland, a humorous dictionary of clichés, Diane Wynne Jones said it all:
"Few NAMES in Fantasyland are considered complete unless they are interrupted by an apostrophe somewhere in the middle (as in Gna’ash). The only names usually exempt from apostrophes, apart from those of most WIZARDS, heroes, and COMPANIONS on the Tour, are those of some COUNTRIES. No one knows the reasons for this."
Including, more often than not, the writers themselves.