The Olatunji Concert: The Last Live Recording

When does something become so altered that it ceases to be what it was? At what point does the stretching, warping, expanding, and "destruction" of something change its identity? Is that something for the observer to decide, or is the power to assign identity solely in the hands of the creator? Can a musician so fundamentally recreate a composition, give it the same name, and have it remain that thing?