The Mayan collapse occurred 700 years before the Inca Empire was founded (and the Aztec Empire, for what it's worth).
People who live in Peru and study the ruins distinguish three megalithic stonework traditions, with the Inka the least sophisticated. The Inka's predecessors routinely handled rocks of tens, and up to hundreds of tons, slicing them into non-convex polygonal shapes and fitting them like puzzle pieces. The Inka worked only much smaller rocks.
Originally, the king was the Inka. No name for the civilization he ruled has surfaced.