Eugene's dog name:

Roofus

Brian's dog name:

Buster Bluth or BB for short

Brandon's dog name:

Doran the Destroyer or Little Val Kilmer

Matt's dog name:

Steve

Tom K's dog name:

Buddy

Stacy's dog name:

Gonzo

Mark's dog name:

Philtrum, or Phil for short

Erica's dog name:

Mooch

Amy's dog name:

I'd go with Methuselah because of his red eyes. Meth for short

Henry's dog name:

Tim Johnson

Matt's dog name:

Batman

Chelsea's dog name:

Girl: Lola
Boy: Woodrow

Adina's dog name:

Barry or Deborah

J's dog name:

A generic dog like this deserves a generic name like "Oreo."

Ross's dog name:

I can only think two things: Gene, short for generic, or Bounty Hunter so he can be Bounty Hunter the Dog.

Wheels' dog name:

Dooze 2

Ginger's dog name:

Bird

Dusty's dog name:

Perrot

Kevin's dog name:

Mr. Witherhocks

Jamie's dog name:

Fluffy McBarks-a-Lot