The second form is correct, and it has nothing to do with whether it's one or more names. You just use the genitive form.

> Felix’ und Mareikes Hochzeit

For names, the genitive form is normally just the standard form with an appended s.

> Mareike => Mareikes  
> Otto => Ottos  
> Alexander => Alexanders  

However, for names ending in s-sounds, namely in s, ss, ß, tz, z or x, the genitive form is instead the standard form with an appended apostrophe.

> Felix => Felix’  
> Marcus => Marcus’  
> Jens => Jens’  
> Der Roman „Der Butt” von Günther Grass => Günther Grass’ Roman „Der Butt”

The apostrophe has nothing to do with the one in the English genitive, but stands for the "omitted" genitive ending.

In older German, you might also find the older genitive form ending in -ens, but this not in use any more:

> Felixens und Mareikes Hochzeit

In very old texts (as well as in current ones from people who don't care), you may also encounter the possessive apostrophe like in English, see [this question][1].

  [1]: https://german.stackexchange.com/questions/53136/did-german-have-a-possessive-apostrophe