The Union Army had dozens and dozens of generals.
Ulysses S. Grant was a General, but was promoted to General-in-Chief in March 1964.
Other very notable Union generals included: General William T. Sherman, General George G. Meade, General Philip H. Sheridan, General George H. Thomas, General Oliver O. Howard, General Andrew A. Humphreys, General Abner Doubleday, General Joseph Hooker, General Ambrose Burnside, General William S. Rosecrans, General Don Carlos Buell, and General George B. McClellan.
All of these Generals held important commands during the American Civil War.