What was the first phase of the proposed Allied invasion of Japan called?

The first phase of the proposed Allied invasion of Japan was called Operation Olympic.

Operation Olympic was planned as the invasion of southern Kyūshū, Japan's southernmost main island. It was scheduled to begin in November 1945 and would have used Okinawa as a staging base. The objective was to seize territory and airfields that could support a later invasion of the Kantō Plain near Tokyo.

Olympic was the first part of the broader Operation Downfall plan. The second phase, Operation Coronet, was planned for Honshū in spring 1946. Downfall was canceled after Japan surrendered, following the atomic bombings of Hiroshima and Nagasaki and the Soviet declaration of war.

These operation names are often mixed up. Downfall was the overall invasion plan, Olympic was the Kyūshū phase, and Coronet was the planned Honshū phase. Japan had its own defensive plan, Operation Ketsugō, designed to resist the expected invasion.