Final answer:
J. Edgar Hoover became director of the bureau of investigation in 1924 and the agency was renamed the Federal Bureau of Investigation in 1935.
Step-by-step explanation:
J. Edgar Hoover became director of the bureau of investigation within the Justice Department in 1924. At that time, the agency was still called the Bureau of Investigation. It was not until 1935 that the agency was officially renamed the Federal Bureau of Investigation (FBI).