My name in SS is Hikari, becauseI cosplay Hikari/Dawn. And besides, I just love the Japanese name Hikari.
My rival is Vincent. Random name that I thought fit him well.
I don't nickname my Pokemon. I used to, but sometimes it would irritate me that my Pokemon aren't their original names, so I quit naming them. Don't know why it bugged me, but it did.
As for my team, it varies depending on what I am doing. For example, if I'm out in the field catching Pokemon or searching for items, I carry around my field team. My team that knows all the field moves that I may need. This team is usually: Feraligatr, Noctowl, Victreebel, Steelix, Ampharos, and an additional one that varies from time to time - Typhlosion/Roserade/Raikou/Lugia/Arceus.