Answer1

'Pap' or 'Uncle George'	Fondly given by his men. His men trusted him not to needlessly risk their lives in no-hope attacks (unlike many other union generals who were pressured into doing some tragic things). His men knew he would have the odds in their favor with superior planning, tactics, and resources in place, and having done so, he would expect each of them to do their utmost to defeat the enemy and help end the war. This resulted in some spectacular actions such as the spontaneous charge up Missionary Ridge. Only a Thomas inspired army could pull off such a feat of arms. Thomas resisted Grant's urging for an early attack until he knew that Hooker's men were close to flanking Bragg's position from Lookout Mountain. With one eye on Hooker and seeing the daring frontal attack pressed home with vigor, the Confederate line dissolved. A similar attack was not successfully accomplished by any other army - North or South. At Nashville he was quite willing to be fired rather than send his men out to attack during an ice storm which would have needlessly raised the number of casualties and might lead to an inconclusive battle. He hated inconclusive battles because he knew that it only meant that another battle would need to be fought with additional loss of life.
'Old Thom'	Given by his fellow Cadets at West Point as he seemed more mature than the rest and he was slightly older than most of them (not quite twenty when he started). Most of the officers during the war may have referred to him this way, but probably only General Sherman his old roommate could say it to him directly.
'Slow Trot'	Used by General Grant as a put-down during the Civil War but actually has its origin when Thomas was the cavalry instructor at West Point. The horses available at the Point in 1852 were very old and to keep the enthusiastic cadets from killing them, Thomas would shout the command 'Slow Trot, Slow Trot' to them during riding drill. Later when Robert E. Lee became Superintendent, Thomas was able to get better horses. Thomas never rushed but was not slow. When the day set for the start of the Atlanta campaign came, for example, Thomas' army was in the field, fully equipped and ready to go. The other two smaller federal armies were not.
'The Rock of Chickamauga'	The first usage of this term may have come from General James A. Garfield (future president). Garfield, after he had joined Thomas on Horseshoe Ridge, dispatched a message informing Rosecrans in Chattanooga that Thomas was fighting off the Confederates and was "standing like a rock". Reprinted in newspapers all over the country, the message made a national hero of Thomas, who would be known for the rest of his life as the "Rock of Chickamauga." Also, Secretary of War Stanton later wrote: "You stood like a rock and that stand gives you fame which will grow brighter as the ages go by."
'The Hammer of Nashville' or	His greatest battle.
'The Sledge of Nashville'