Zeppo is a minor character only appearing in Pinky & The Brain... and Larry.
Much like Larry, Zeppo was called to be the third lab mouse after Larry left, much to the dismay of Pinky and Brain. During the ending song, much like the beginning, he would add his name in open spots ("They're dinky. They're Pinky & the Brain (and Zeppo), Brain (and Zeppo), Brain (Zeppo), Brain (Zeppo)!")
Zeppo's name comes from the Marx Brother of the same name.