Not much backstory of the teen has been disclosed in either the Simpsons TV series or the comic books. It was revealed in Season 7's episode Team Homer that he is the son of Lunchlady Doris, although this was never referred to again other than for the purpose of one joke. In a deleted scene from Season 5's Sweet Seymour Skinner's Baadasssss Song, both the character's name and the fact he was a former student at Springfield Elementary were revealed but neither is considered canon as the scene didn't make the final cut.
The Pimple Faced Teen, also frequently known as the Squeaky Voiced Teen, was created by Matt Groening and Simpsons writer John Swarzwelder and first appeared in the Season 3 episode Dog of Death as a student at barber college. In the show he is voiced by Dan Castellaneta. His first appearance in Simpsons comics was in Bart Simpson's Treehouse of Horror #3.
Grampa Simpson referred to him as "old man Peterson" but this is not a reputable source considering Grampa Simpson is pretty much suffering from some form of dementia most of the time. His name was revealed as Jeremy in a deleted scene from Season 5 but as the scene was removed from the episode, it isn't considered canon. In an episode where the bullies Jimbo, Dolph and Kearney work at a shoe store, they refer to him as Mr. Freedman. In the episode: "Beware My Cheating Bart" he has a nameplate that shows his name is Steve.
The running joke with the character is that he is routinely shown in dead-end menial jobs such as working at fast food restaurants, bowling alleys, theaters, supermarkets and so on. Most frequently he is shown to be working at Krusty Burger, where his role has ranged from a cashier to a cook and in one episode supervised trainees. The running joke from the show continues in the comics where he is again seen popping up in various different jobs across Springfield.