There are several good web sites on the Manhattan Project. It seems that it got that name in 1942.
The Manhattan Project, or more fully, the Manhattan Engineering District Project, was an effort during World War II to develop the first nuclear weapons by the United States with assistance from the United Kingdom and Canada. Its research was directed by American physicist J. Robert Oppenheimer, and overall by General Leslie R. Groves after it became clear that success was possible and that Germany was also investigating that possibility.
Though it involved over thirty different research and production sites, the Manhattan Project was largely carried out in three secret scientific cities that were established by power of eminent domain: Hanford, Washington, Los Alamos, New Mexico, and Oak Ridge, Tennessee. Some families in Tennessee were given two weeks notice to vacant the family farm lands they had had for generations. The existence of these cities was offically secret until several years after the war.
In the summer of 1942, Col. Leslie Groves was deputy to the chief of construction for the Army Corps of Engineers and had overseen construction of the Pentagon, the world's largest office building. Hoping for an overseas command, Groves objected when Somervell appointed him to take charge of the weapons project. His objections were overruled and Groves resigned himself to leading a project he thought had little chance of succeeding.
The first thing he did was rechristen the project The Manhattan District. The name evolved from the Corps of Engineers practice of naming districts after its headquarters' city (Marshall's headquarters were in New York City). At the same time, Groves was promoted to brigadier general, which gave him the rank thought necessary to deal with the senior scientists in the project.
The Manhattan Project
During the Second World War, the United States and Britain jointly participated in the monumental task of building an atomic bomb. The project was code named the "Manhattan Project" to obscure its purpose, and because the first meetings were conducted in Manhattan.