How many different commanders did the union army in the first two years of the civil war?

Each side had several different field armies, fighting in various parts of the country. The armies people are most familiar with today are those which were fighting in the east, that is, east of the Appalachian Mountains. For the north their field army in this theater was the Army of the Potomac, and for the south their field army opposing the Army of the Potomac was the Army of Northern Virginia. But each of these was only one of the several field armies fighting for their respective sections. The commanders of the northern Army of the Potomac in the first two years were Irvin McDowell, George B. McClellan, John Pope, McClellan again, Ambrose Burnside, Joseph Hooker, and George G. Meade.

The north did have an overall commanding general in Washington DC. At first this was ancient Winfield Scott, then McClellan, trying to be both general-in-chief as well as field commander of the Army of the Potomac. McClellan would not do much so Lincoln brought Henry W. Halleck from the west and made him general-in-chief, but he didn't really work out either. Grant was brought east in 1864 and made general-in-chief. He did not stay in Washington, nor did he replace Meade as commander of the Army of the Potomac. Meade continued to command that army, but Grant traveled along with it and made his headquarters with Meade's army, providing daily supervision of Meade's activities.

The south for almost all of the war had no general-in-chief in overall command. Jefferson Davis, Confederate president, was a West Point graduate and mostly acted as his own general-in-chief. As the war kept going worse and worse for the south the Confederate congress finally forced Davis to make Robert E. Lee general-in-chief, as well as field commander of the Army of Northern Virginia. This was only two months before the end of the war and far too late to do any good.