I think, rather than the FN designation coming from Finn’s …

Comment on Force Awakens Toys Leak Dialogue by Mat W.

I think, rather than the FN designation coming from Finn’s name, Finn’s name is supposed to come from his designation. If you watch THX 1138, you’ll notice that Robert Duvall’s character is called “Thix”, from the letters of his designation.

I think the person Finn regrets rescuing isn’t Rey, but Poe Dameron, who is captured at some point by the First Order and later escapes with Finn in a Tie Figher, presumably with Finn’s help.

Fun Fact: Leia’s cell number is a reference to the short film, 21-87, which was an inspiration for Lucas’s short film, Electronic Labyrinth THX1138 4B.