No, they are not related. The only thing they have in common is their last name.

John Edgar Hoover was the first Director of the Federal Bureau of Investigation (FBI) of the United States. Appointed director of the Bureau of Investigation—predecessor to the FBI—in 1924, he was instrumental in founding the FBI in 1935, where he remained director until his death in 1972 at age 77. Hoover is credited with building the FBI into a larger crime-fighting agency, and with instituting a number of modernizations to police technology, such as a centralized fingerprint file and forensic laboratories.

Herbert Clark Hoover was the 31st President of the United States (1929–1933). He was a professional mining engineer, and was raised as a Quaker. A Republican, Hoover served as head of the U.S. Food Administration during World War I, and became internationally known for humanitarian relief efforts in war-time Belgium. As the United States Secretary of Commerce in the 1920s under Presidents Warren G. Harding and Calvin Coolidge, he promoted partnerships between government and business under the rubric "economic modernization". In the presidential election of 1928, Hoover easily won the Republican nomination, despite having no elected-office experience. Hoover is the most recent cabinet secretary to be elected President of the United States, as well as one of only two Presidents (along with William Howard Taft) elected without electoral experience or high military rank.