The Commander in Chief was President Abraham Lincoln.
The Generals in Chief were:
Lieutenant - General (honorary) Winfield Scott, substituted by
Major General George Brinton McClellan, substituted by
Henry Wagner Halleck, substituted by
Lieutenant General Ulysses Simpson Grant starting from March 9, 1864
Grant commanded the Northern army during the US Civil War. Giap commanded the Northern army during the Vietnam War.
Yes, he commanded the Army of Northern Virginia.
The Army of Northern Virginia
Lee commanded he Army of Northern Virginia. Mead commanded the Army of the Potomac.
The Army of Northern Virginia was commanded by Robert E. Lee
General Lee did not "surrender the Civil War". He surrendered his army, the Army of Northern Virginia, when it was clear that he could no longer effectively fight against the Army of the Potomac commanded by Ulysses Grant.
Robert E. Lee
Thomas J "Stonewall" Jackson commanded a corps in Lee's Army of Northern Virginia.
Meade commanded the Army of the Potomac (Union). Lee commanded the Army of Northern Virginia (Confederacy).
Robert E. Lee
The Army of the Potomac was commanded, in turn, by Irvin McDowell, George McClellan, Ambrose Burnside, Joseph Hooker and George Meade. As this was the army that ended the war by defeating the Army of Northern Virginia, some say that Lee should have surrendered to Meade, not Grant.
He was in command of his own Army - the Army of Northern Virginia.