When MGM signed a licensing agreement in the 80s with Disney, they were (once again) in financial turmoil, and so desperate for the agreement that they granted rights to use the MGM name and movie references in perpetuity (that means forever), which means that while Disney could certainly change the name of the park, or reduce the presence of MGM-produced movies within the park, or both, they are not required to at any point ever.
Also, the Great Movie Ride (as well as the rest of the park) features films that were produced by MGM, Warner Bros, Fox, Paramount, RKO, United Artists, Columbia Pictures, and others. MGM does not own any rights to The Wizard of Oz (nor does their current owner, Sony). Turner bought that film along with many others in the MGM library years and years ago, and then Turner merged with Time Warner back in the 90s. Niether deal affects the use of Oz in GMR, however.
The idea that "The MGM contract is about to run out!" is pure internet hokum.
A very good point has been made about an MGM theme park opening in Asia being a viable reason for Disney to want to disassociate their Studios park in FL from that brand, however.
Also also... I like "The Disney/ABC Studios" personally...