A bit of more context of this scene:

This takes place in Demo's house, they're all having a sleepover there. By this time, Soldier has already ran away from home and stayed at Demo's place (to protect him from his father). In this period of time, Soldier doesn't want to go out that much because of paranoia and skepticism, so all of his friends gather at Demo's place and even have sleepovers. This warm yet funny scene has more depth considering this all takes place in a time where Engie puts his feelings aside to focus on Soldier's well-being. They grow closer, and in this sleepover Soldier wants to go out and feel the rain in the middle of the night, the only one awake was Engie and he goes with him (concerned). They have a sweet yet fun moment running in the rain and thus, this scene happens.

The way Soldier comes up with each codename is with the way everyone behaves or the skills that they've shown so far.

Scout, he usually climbs whatever to have a better view to ensure it's safe for Soldier to move around the school (since he isn’t part of it).

Pyro, they already have that nickname, but Soldier knows it's because their fixation with fire.

Medic, the one that has the ambition and knowledge to be an actual medic in the future, he's usually the one patching his friends up or showing his vast knowledge about his future major.

Demo, he's Soldier's childhood friend, and he knows Demo is really into chemistry because of his parents. When playing videogames he always picked explosive weapons, hence the nickname.

Heavy, he's a big guy and Soldier has seen how truly strong he actually is, he's like a rock, unmovable, but a softie inside. He considers him the tank of the group.

Sniper, he loves causing playing with his slingshot, so one day Soldier saw what great aim he has with it and so he called him by that. What a compliment, and makes him sound badass.

Engineer (Engie), he's the smartest of the group, not only that but he's always seen carrying tools in his bags, welding goggles in his backpack and when loves spending time in the school's workshop.