These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crowning Moment of Funny: He got hit in the face by a fan-thrown coconut cream pie during one concert, while crouched theatrically over a devil shrine. The amazing part is, he stayed in character, dipping a finger in the pie filling and licking it off while wearing a Slasher Smile.
From "No More Mr. Nice Guy": I went to church incognito/When everybody rose/The Reverend Smithy/He recognized me...and punched me in the nose!
He changed his name to Alice Cooper because it was the best way to retain legal rights to its usage. Thus, the music company that the band worked for wouldn't be able to hold on to the rights. For contrast, see "the artist formerly known as Prince," who after switching companies became legally unable to use his original stage name.
This actually turned out to be unnecessary because he bought the band name, as well. Which means he was also able to trademark "Alice Cooper," which he would not have been able to do if it solely referred to him. Band names can be trademarked, but a person's name can't.
No Such Thing as Bad Publicity: During a 1969 concert in Toronto, Cooper picked up a chicken someone had thrown onstage and tossed it back into the audience, thinking since the bird had wings, it would fly. Instead, it plummeted into the audience, who promptly tore it to shreds. This story quickly mutated into a rumor that he'd actually bitten the head off the chicken himself. Cooper received a phone call from Frank Zappa asking if he'd done so. When he replied that he hadn't, Zappa said, "Well, don't tell anybody you didn't do it!"