Sydney doesn't actually battle - she doesn't have a single badge. She's pretty unoriginal with names, so most of her pokemon don't have nicknames at all. She doesn't really catch pokemon either; instead they're pretty much all abandoned or orphaned pokes who end up fitting in well with her little bundle. In some way or another they're all rehomed. Sydney's really good at keeping the peace throughout her "team", so all her pokemon get along well with one another.

Vaporeon was her first official pokemon, and latched onto her pretty hard. He's an old boy now, and takes a backseat to most of the antics, generally he just keeps a watchful eye over things and it's fairly rare for him to join in nowadays.
Kitkat came to her as a Buizel, and hasn't matured much despite his evolution; he's still just as silly and snuggly as ever, always looking for attention from her. Sometimes Sydney catches him and Mienshao together even though Mienshao pretends to be above his silliness.
Mienshao is a bit of a flirt who loves being pegged! He pretends to be high-and-mighty a lot of the time, though.
Dippy is a big sweetheart who's quick to help break up fights around the ranch. She functions as a bit of a team mom. She's laid back and positive, and her and Sydney love to team up on grumpy pokemon to help ~ease their frustration~.