Shane is a backgrounder at Lawndale High and a student in the same year as Quinn Morgendorffer. He's a tuckerization of Daria production assistant Shane Guenego. Officially he goes unnamed but a seating chart for his class in "Cafe Disaffecto" names a "Shane", taken to be a nod to him/Guenego. Previously, he was nicknamed "Butt-head Two" on the website Backgrounders.
He first appeared in "Too Cute", where Quinn asked for money for cosmetic surgery: he responded with a Butthead-esque laugh. His other big moment with Quinn was to act horrified and look for help when she answered a question correctly in class in "Is It Fall Yet?".
In "Lucky Strike", Shane was taught by Daria and, like the rest of the class, left dismayed by the sound of a test. Despite this, and his looks, he smiles at his returned paper: we don't know what his mark was but he considered it a job well done.
As well as looking and sounding dopey, he's a bit of a delinquent too: he's friends with another trouble-maker, "Red Cap" and the two ran around spraying silly-stringer at a defenceless Daria and Tad Gupty in "I Loathe a Parade". The two of them are big fans of Mental in the Morning and followed the DJ's around Lawndale High.
His other friends include "Jackass" and "Beehive Girl" (she joined him and Cap in spraying Daria).
Shane in fanfiction
Shane made his fic debut in 2010, when he was grabbed at random and made into a member of Quinn's Maleficent Eleven gang in "God Save The Esteem" by Charles RB ("Butt-head Two" being what Quinn instinctively calls him). He then surfaced as a midcard wrestler in The Excellent S's "Lawndale Fighting Championship" series, sometimes tagteamed with Rob.
He (along with Jackass #2, who gets the name Mason) appears at the beginning of WellTemperedClavier's The Background Blues. Shane's ill-advised attempt to smoke pot indoors starts a fire in the school auditorium, which gets the whole plot rolling.
Butt-head Two (Shane) at Backgrounders (Wayback)
The Transformed Staff flipbook (Wayback), his page sadly lost
Daria: The Transformed Staff overview at the Daria Fandom Blog