I believe Aphex Twin's label Rephlex called it braindance originally. I've always liked their description: "braindance is the genre that encompasses the best elements of all genres, e.g traditional, classical, electronic music, popular, modern, industrial, ambient, hip hop, electro, house, techno, breakbeat, hardcore, ragga, garage, drum and bass, etc."
IDM first gained mainstream attention with the Warp records compilation album "Artificial Intelligence", which called it "electronic listening music." It's a pity this name never caught on, because it's more accurate than IDM. Wikipedia quotes Warp co-founder Steve Beckett:
"You could sit down and listen to it like you would a Kraftwerk or Pink Floyd album. That's why we put those sleeves on the cover of Artificial Intelligence – to get it into people's minds that you weren't supposed to dance to it!"
