I named myself: Slick. This has been my name in the games for 2 generations. I always like playing as the boy.
My rival: Lucas. What I have named my rival in the past as well but not always.
Emboar: Spunky. He most definitely is!
Froslass: Shiva. Pretty obvious but I think it suits her beautifully.
Beheeyem: Jedi. I'd like to think he uses The Force for his power :3
Excadrill: Excaliber. Because he is strong and the name came to me from the beginning of his species name.
Ampharos: Fender. My mind went to the coolest electric object I could think of. She's a girl but it suits her well.
Azumarill: Unfortunately my Huge Power water rabbit is nameless. Anything I thought of seemed so cliche I didn't want to give them to her. Will edit if I ever decide on one.