With all the mind-wiping and reconditioning, Stormtroopers don’t have very reliable memories. The only way to ensure that they remember important things is to write themselves notes in code/using symbols … on their skin. (Up to filler if the Stormtroopers use scars, tattoos, or something else.)

By this time in his life, half of Finn’s body is covered in these permanent marks. So when Poe first sees Finn naked, that’s what he sees.

+1: Poe misunderstands the marks and suggests getting them removed; Finn freaks out.

+10: Finn tells Poe some of his stories.

+100: Finn reads the stories of defecting/captured Stormtroopers through their marks.

+1000000: Finn makes a note on his skin to remind him of Poe.