Mistaken identity is another classic story element that can be utilised in a game setting. The most obvious use is to have random NPCs mistake PCs for someone they know, resulting ins some confusion and hilarity.
The other way to do it is to tell the players that their characters see someone they know. They might spot the blacksmith from their village while wandering through a city, for example. If they go over and attempt to say hello, the person is momentarily confused and claims not to be the person they know.
Are they telling the truth? Why would they be lying? If they are telling the truth, why is there someone identical to the blacksmith wandering around?
Commentary by memnarch (who has not seen the movie)
Ok, nope. Definitely not a twin situation in the movie then. Even if I can't figure out a good reason why a spy and a (probably still) brainwashed spy would be hugging, there's even less reason for a spy and the twin of a brainwashed spy to be hugging. And as a reminder (which I needed to look up myself), the last time we saw the two together in the comic, Finn said he was going to kill Poe after everything was over. Finn really doesn't look the type to want to kill someone over again just because they don't like them, so that feels like something that needs resolving before hugs happen.
Jim is definitely getting into the fake twin thing. "Allan" reminds me of Han's description from a while ago; I wonder if Jim is playing his character as having Prosopagnosia of some form as well in this case. And of course, fraternal twins are a thing, so that wouldn't be an impediment to thinking that kind of a relationship exists either.
Commentary by Keybounce (who has not seen the movie)
[Keybounce's comments will appear here when received.]
GM: Finn, you see BB-8 talking to what looks like Poe.
Allan: I run over and hug him!
Allan: Poe, my man! Good to see you!
Finn: Poe! You’re alive! Wait... what??
Finn: You’re Poe!
Allan: Pretty sure you are. I’d recognise that jacket anywhere.
Finn: What about this face? Do you recognise this face?
Allan: Yeah, I always thought you were the ugly twin.