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I always nickname my Ditto by their nature and IV spread.
I'll also nickname my competitive mons with names which might throw off the opponent by bluffing a set (something like calling Expert Belt Mega Ray "Band from Ubers" to fake a choice band) or irritating names (so they get angry while getting PP stalled out by "u lose xd" the Dusclops)
Other than that, I avoid it. I only really see nicknames as a way of communicating with the opponent, so spending my time naming my Infernape "Luffy ;3" or whatever is just stupid bullshit.