TheBuskersDog -I think people misuse the word nickname because it's just easier, although not strictly the correct word.
Especially in a case like this when a theoretical conversation goes something like:-
Stranger: 'What's your name?' Johnny: 'Johnny' Stranger: 'Oh what a lovely name. Is that short for Jonathan?' Johnny: 'No, it's short for John. Oh I mean it's actually long for John. Oh that doesn't make sense. It's a diminutive of John'