What do you call a 'Nickname' that's longer than the actual name?

I’m pretty sure I used to know the term for a nickname that was longer or an expansion of a person’s name.

EXAMPLE: My name is Sunny but friends sometimes call me Sunshine.

Though longer, Sunshine is still a nickname since nicknames don’t have to be shorter than the original. But I’m sure there’s a specialized term for this sort of reverse construction. Help!