Jeremiah the Greninja, because I can't understand a word he says.
Jawson the Tyrantrum, because I like the way it sounds.
Rex the Venusaur, because I didn't have Tyrunt yet, and I couldn't think of a better nickname.
Tibia the Marrowak, because it is equal parts fitting and feminine.
Nibbles the Gabite, because it's equal parts subversive and fitting.
Slow Sista' the Slowpoke, because both her evolutions names were unfitting for a female.
Larvly, a pun on "lovely" and "larva" for my Vivillon.
Wally the Snorlax, because he looks kinda like a Wally.
Picasso the Smeargle, for obvious reasons.
Tank the Rhyhorn, for slightly less obvious reasons.
For some reason, I haven't nicknamed a couple of my team 'mons, including Swalot (though I'm not the OT, so I'm not sure if I can) and Helioptile, since I can't think of anything good.
Lastly, there's my pride and joy when it comes to nicknames, Margarine the Butterfree.