Exactly as the title says. I caught some Pokemon, nicknamed them, checked them in the PC and they didn't have any nickname. I know the PC supports storing nicknamed Pokemon as it keeps the nickname of a Pokemon I deposit from the party, so it seems it just doesn't record it if you nickname a Pokemon and it gets sent to the PC after battle.
EDIT:
changed to have proper grammer, as per the post rules.
EDIT:
changed to have proper grammer, as per the post rules.
