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Weight Watchers = Blissey (who really isn't fat; only 103 pounds, which is appropriate for 4'11'')
H5N1 = Cresselia (H5N1 is avian flu, and Cresselia is a space duck)
I usually choose nicknames that are of some relevance to my poke:
Garchomp = "Kauhuhu" - A vicious shark king taken from Hawaiian mythology.
Weezing = "Carcinogen" - A cancer causing agent.
Mismagius (F) = "Bozaloshtsh" - From Wendish mythology meaning "Lady who Cries". Is a female ghost/spirit who would appear when death is certain and release a howling cry. See Mismagius' PokeDex entry to see why I choose this name.
Swampert = "Lahmu" - First born son of Babylonian goddess Tiamat. Name mean's "The Muddy One".
Gyarados = "Grennian" - Old English for "Gnashing of Teeth".
There's tons more that I use, these are just examples.