How do I register friend codes from Pokémon Sun/Moon?

Unfortunately, you can't register friends directly from Pokémon Sun/Moon. What you can do, though, is mark trainers as VIPs in your plaza, so you can find them easily later. You can do this by talking to the trainer you want to register within your plaza, and picking the option 'I'll add you as my VIP' (or something like that, I don't remember the exact wording).

The last trainer you battled/traded with will be standing inside the central castle, just to the left of the middle of the room. You can easily register them as a VIP from there. VIP trainers will never leave your plaza, and can be found on a separate menu when looking to battle/trade directly, for easy access.

Friends you've exchanged codes with in previous games won't be saved separately like VIPs, so you'll still have to find then manually. But if you and a friend are online at the same time, and you look for them to battle/trade, the menu