The Union field army involved was the Army of the Potomac, at that time under the command of Major General Joseph Hooker. Under "related links" below is a link to a Union "Order of Battle" for the Army of the Potomac at Chancellorsville which lists all units in a particular command at a certain moment in time.
Shiloh
The Battle of Antietam, an important battle of the Civiil War, was fought by the Army of the Potomac, part of the Union Army, under the command of General George McClellan, and Confederate forces under the command of General Robert E. Lee on September 17, 1862.
General Joseph Hooker was in the Union Army. He reached his peak during the War in the Spring of 1863 when Lincoln appointed him to Command of the Army of the Potomac. His term of appointment was short-lived as the Union Army under his Command was routed by the Army of Northern Virginia Commanded by General Robert E. Lee at the Battle of Chancellorsville. He was replaced by General George Meade.
One of the outstanding victories of the Confederacy occurred at the Battle of Chancellorsville. Even though Jackson's army was severely outnumbered, Lee and Jackson coordinated their forces and defeated the Union army under the command of Major General Joseph Hooker.
No he was in command of the Army of Northern Virginia.
Robert E. Lee
I believe General Meade was in command of the Union's Army of the Potomac.
General Tecumseh Sherman, was the Union General who ransacked the South, all the way to the sea. He took over the Union Campaign in the west after General Ulysses S. Grant took over command of the Union Army, or the Army of the Potomac.
Major General George G. Mead was in command of the Union Army of the Potomac at Gettysburg.
The command of the Federal Army of the Potomac went to Major General Joseph Hooker after Fredericksburg.
The Union Army of the Tennessee was commanded by Major General Ulysses S. Grant on April 6, 1862, the first day of the battle. This army would be reinforced by the Army of the Ohio under the command of Major General Don Carlos Buell the evening of the 6th and Grant took overall command of both. The Confederate Army of the Mississippi was commanded by General Albert Sidney Johnston on the first day until he was killed, then command of the army fell to General P.G.T. Beauregard who commanded for the remainder of the battle.