The story
Coined by Alvy Ray Smith and Ed Catmull in the 1970s. Smith writes: "We called it that because of the classic linear interpolation formula αA+(1-α)B that uses the Greek letter α (alpha) to control the amount of interpolation between, in this case, two images A and B". That is, when compositing image A atop image B, the value of α in the formula is A's alpha channel.
Etymology from Wiktionary, CC BY-SA 4.0.