Okay, I have to admit I'm somewhat confused.
Three different sources:
Example #1
NOTE: Although names ending in s or an s sound are not required to have the second s added in possessive form, it is preferred.
In other words we should write Jonas's. (the spell checker here doesn't quite agree)
Source: Apostrophes | Punctuation Rules
Example #2
"The apostrophe in a word like parents' does not change the pronunciation at all. But with singular classical (ancient Greek and Roman) names ending in s', we often pronounce a possessive 's even when it is not written.
In other words: Socrates' ideas.
Source: Practical English Usage, 3rd Edition, 439.2
Example #3
"If the singular noun has more than one syllable, add only an apostrophe:
....Jesus' disciples"
Source: Barron's ESL Guide to American Business English, p. 256
The Dilemma
I have to say that I've been erring on the side of not using the apostrophe when a name ends with an s. In other words, Jess' and not Jess's and Tess' and not Tess's. For some odd reason, it just felt right. Now I'm utterly confused and feel that I've been misleading my students. Given the examples above, there seems to be no clear-cut answer, although the use of 's seems to be more popular.
What's your take, guys?
Omission is the most popular because it is the easiest. However, I do prefer to see 's as more representative of pronunciation.
I have to teach this to students who are in their first year of learning English and they have the problem, that we have a "possessive -s" in German, too, but without apostrophe.
So in order to avoid confusion, I teach them " 's" for one person and only apostrophe for more than one:
the girl's book, the girls' books
The rule also applies to names: James is only one person, so James's book
Parents is a plural word, so "parents' ".
When they write, I silently accept "James' sister" , too.