Apostrophe in names does not really relate to missing letters, but rather glottal stops or syllable breaks in order to pronounce them correctly. There are plenty of real-world cultures which have names with an apostrophe, but in fantasy or sci-fi it is used as a way to make a name or word appear more alien.
For example Laezel sounds less alien than Lae'zel. Another example would be Star Trek in which you have the Klingons and their words sound like this;
- d'k tahg
- Fek'lhr
- Ghay'cha'
- Qapla'
