I have a question, teacher!
Why was the singer's name Alice?
"Listen, baby, you really wouldn't understand ..." is NOT an acceptable answer to this!
If my addled brain remembers correctly, it was for the shock value. Shep Gordon became their original manager after he saw The Troubador EMPTY out in a matter of minutes when Alice Cooper played there early on. They were not the Joni Mitchell copy that the audience was hoping for. Gordon said that any band that could do that had some definite marketing potential. As I recall, it was Gordon himself who called Canadian officials and warned them about the "flammable" panties that were the album sleeve for School's Out, and then milked the publicity.
According to classicbands.com:
Although it has been rumored for years that the band took its name after consulting a Ouija board, vocalist Vincent Furnier said in an interview with the VH1 TV series Behind The Music "I remember we were sitting around talking about band names. I was eating Doritos and just said the first name that came to mind. Which was Alice Cooper."