Kachina - (1971-1972) - Kachina the first snake and she was the 'Killer' cover girl. Kachina perished down a toilet drain in a Tennessee hotel room during the 'Killer' tour. She was actually owned by Neal Smith (who still owns snakes to this day).
Yvonne (1972 'School's Out') - There was a rumour saying she almost suffocated Alice one night while he was preparing her for the stage, and that security guy Norm Klein cut her head off to free Alice. It's not true, just another story created for the publicity.
Eva Marie Snake (1973 'Billion Dollar Babies' tour) - Eva was named after a movie star (Eva Marie Saint).
Angel (1977 - 1979(?)) - Angel was the winning snake in a competition held in Anaheim in 1977 to find Alice a snake for the 'King of the Silver Screen' tour. She died when she was bitten by a rat during dinner time.
Veronica (?) - Alice spoke about a snake named Veronica during various radio interview, but it seems to have just been a name he threw around. Of cours ethe name of the snake in the first Marvel comic book was 'Veronica'.
Mistress (1986) 'The Nightmare Returns' tour (Credited on the back of the video).
Lady Macbeth (1998) The 'Rock and Roll Carnival' Tour. In fact, Lady Macbeth was the snake that was supplied for the European Tour by Sickthing Bill Crowe. They continued using the name on the US leg, but it was a different snake. In 2003, Bill got the call again and Lady Macbeth (the exact same snake) returned to active duty for the 3 UK Bare Bones shows in July. Again, a different snake was used in the US show and no snake was used in the mainland Europe gigs. Unfortunately she died in the mid 2000's and Bill obtained a new snake, Dali, who was used in subsequent UK and European appearances. Sadly Dali also passed away in 2013.
Since at least around 2000 when a snake is required Alice has generally made use of borrowed local snakes, changing as he moves around the world. He no longer owns a permanent snake.
Others information from Brian Nelson:
The House Of Blues Show
Alice Cooper has been using snakes in the show for thirty years with few problems, until a show at the 'House of Blues' in Los Angeles in August (19th?) 1998, when it decided to relieve itself all over the floor.
The Heating Pad Incident
While on tour in the USA in August 2004, the hired albino snake being used during the show had an unfortunate mishap. When the snake was fed it managed to eat its heating pad as well. Here is the full story as reported by the owners of the snake at Amazon Reptile Center