Short answers, pulled from the story.
Army correspondence began using the term "Army of the Tennessee" in March 1862, describing troops under Ulysses S. Grant in the District of West Tennessee. The name became official in October 1862, when Grant's command was elevated to departmental status as the Department of the Tennessee.
Ulysses S. Grant commanded the army from its formation until after his Vicksburg victory on the 4th of July 1863. William Tecumseh Sherman succeeded him, followed by James B. McPherson, John A. Logan, Oliver O. Howard, and finally Logan again from May 1865.
The army fought at Belmont, Fort Henry, Fort Donelson, Shiloh, Corinth, Vicksburg, and Chattanooga. It also fought throughout the Atlanta campaign, including the Battle of Atlanta and Ezra Church. It later marched in the March to the Sea and the Carolinas campaign, fighting at Bentonville.
William Tecumseh Sherman said in 1867 that the army was always victorious and so rapid in motion that it deserved the name Whip-lash. He described it as being swung from one flank to the other, wherever danger called, during the Atlanta campaign.
Taps sounded for the Army of the Tennessee on the 1st of August 1865. This followed the Grand Review in Washington, D.C., on the 24th of May 1865. Its veterans later formed the Society of the Army of the Tennessee, organized on the 14th of April 1865.
McPherson was killed on the 22nd of July 1864 during the Battle of Atlanta. Confederate General John Bell Hood had launched a strong assault against his army on Sherman's left flank. McPherson was later buried at Clyde, Ohio, where the Society of the Army of the Tennessee placed a memorial.