The castle in the MK is "Cinderella Castle" ... not Cinderella's Castle (this one doesn't really bug me much, but it bugs some other folks I've talked to.
I think there's a lot of names that get shortened ... In casual conversation, I'm a lot more likely to say "I went over to MGM and rode Coaster"" than I am to say "I went over to the Disney-MGM Studios and rode the Rock N Roller Coaster, starring Aerosmith". In a similar manner, I will usually refer to "Space", "Splash", or "Big Thunder" rather than adding the "mountain" on there.