>>15773976The technical reason as to why traded Pokémon cannot be nicknamed is because their ID number and OT (Original Trainer) do not match those of the player.
In Pokémon Yellow, the player can cheat to get another starter Pikachu (= Pikachu with the same ID and OT as the player) which will behave like one after the original starter Pikachu is released. This applies to multiple starter Pikachu as well, as only one will behave like the starter Pikachu. Furthermore, if you add more starter Pikachu without releasing the original one, then delete the new ones, the original one will have a disappointment face for a limited period of time.