Just a quick thought, I guess.
I've always kept them as the default names, calling them anything different always felt wrong.
Did you rename your Pokemon when you got them, and if so, why, and what did you name them to?
Also, bonus question, when playing the Final Fantasy games, did you name your characters? As I believe, (don't cull me if I'm wrong), but you could name them in everything up till 10, and in 10 you could only name your title character (in which the other characters awkwardly never say his name.)
Strangely enough I always name my title character after myself, and when I was far younger I used to name everyone else after people I knew, but now it's only the main character. Barrett can stay as Barrett. <3