Alternate Universe and how Folks React

A popular meme in science fiction is the concept of alternate universes. A group of characters encounters some magic or scientific handwaving that results with them interacting another group that hails from a universe where everything is slightly different; a different cultural ethos prevails, a central character died or survived some catastrophe. Most writers have the characters being fairly freaked out and not dealing with the situation well. But what if the characters came from a large family? 
Is there suddenly someone in your life that looks a lot like you, shares the same (or a very similar) name, and is slightly different? To any one who interacted with an extended family this isn't anything new. This is just cousin Sam at the family reunion. Sharing a face with a stranger is pretty much expected. 
An interesting twist would be most of the crew being freaked out but the one character from a large family just shrugged it off, decides on alternating names and starts calling his/her double 'cousin'.