No, I’m not talking about when your wife won’t let you go out with your friends or your husband doesn’t let you talk to anyone at the office Christmas party. What I’m talking about is how to indicate possession when discussing a single object that belongs to two people.
If two people own or have possession of one thing, put the apostrophe after only the second name. For example, if John and Mary host a show together, we referred to it as John and Mary’s show.
Other examples: Dick and George’s secret plan (one plan that they devised together), Barack and Michelle’s gift to the Queen (they gave her one gift together), and Sherry and Paul’s blog.
If you’re talking about two separate things that belong to two separate people, however, each name gets an apostrophe, as in John’s and Mary’s shows, and Newsweek’s and Time’s front-page stories (each has its own front-page story).
Sherry
Everything Language and Grammar 
A little question: I learnt at school that the plural of the possessive case should be s´, same with nouns or names ending in s, but I´ve also seen s´s. Is that correct?
Thank you.
I’m sorry to say that I’ve seen a variety of explanations. I know that’s of no help to you; if it’s any consolation, it’s not any help to the rest of us either.
Some resources say to always put ‘s even if the noun ends in an s that is pronounced; others say to always only put only the apostrophe if the noun ends in a pronounced s. Still others say that GENERALLY the s is omitted when the word already ends in a pronounced s, so you just use the apostrophe at the end to show possession.
In my view, a grammar textbook is the best guide.
Hello:
What happens with the possessive case when it’s used in proper names ending in -s
e.g.
Luis
Carlos
Gertrudis
Do they take the ‘s? or Do they take the ‘ (apostrophe) only?
Thanks so much