I may have been out of the loop in the late 80s and early 90s, but I never heard of this well-named category of music:
Shoegazing is a style of music that emerged in Great Britain in the late 1980s. The beginning of the genre is said to be Isn’t Anything[?] by My Bloody Valentine, released in 1988 (1988 in music). However, it drew heavily upon synth pop and New Wave artists, as well as electronica, glam rock and other artists like David Bowie, and especially Cocteau Twins and Roxy Music.
Shoegazing is characterized by the use of distortion and fuzz, droning riffs and a Spectorish wall of sound from the noisy guitars. While the genres which influenced shoegazing often used of drum machines, shoegazing often featured live drumming. Shoegazing drummers such as Chris Cooper of Pale Saints[?] and the late Chris Acland[?] of Lush often displayed complex drumming.
The name is very evocative, but that quote doesn’t explain who named it or why. Here’s a longer article on the subject.
DarrenBarefoot.com 
Don’t know who named it, but I think I know why (at least, this is the understanding I got the first time I heard of it many years ago)… The people who liten to Shoegazing music are called Shoegazers because they walk around looking at their shoes all day — hunched shoulders, head down, etc. You know, your generally apathetic indie-music lovin’ slacker. 🙂
I always figured it was because it was typically really droning music and if you watch the people playing it they always seem to be just standing there not moving/looking downwards with their hair over their eyes.
it’s named that due to the bands onstage standing there and staring at their shoes…