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I name any Pokémon I'm planning on using for an extended period of time, whether it's a main team member, an HM slave/other utility, or a Pokémon bred for PVP. Obviously, this works out to a minority of the Pokémon I actually catch/breed, but most of the time, unless I'm breeding, most if not all of the Pokémon I'm currently working with have names.
I have two approaches to nicknames, varying with the game I happen to be playing:
1) Nicknames are whatever damn thing happens to occur to me at the time, so a lot of my Pokémon have names that wouldn't make much sense to people other than myself or my boyfriend.
2) Nicknames are themed somehow. This only ever applies to my main team, and I'm most likely to do it on replays of games rather than my first time through. For instance, the names of my character, my rival, and my Pokémon had a Chrono Trigger theme when I did a Nuzlocke of Blue.
I don't really have favorite names for Pokémon.