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Evolution happens in Wiiware right when you meet the requirements for it. It asks you for a prompt beforehand, and after evolving will then ask if you want to give it a nickname, though I'd assume that option doesn't show up if it already has one, like in Sky.
The IQ skill "しんかしない" (Don't Evolve) is the first in the IQ skill list and prevents the prompt from showing up at all when enabled.