If my memory serves me correct, William was not Cump's first name. His father straight up just named him Tecumseh Sherman. I believe he had his name changed when his father died and Tom Ewing had him adopted.
Hence why People close to him like Grant refer to him as "Cump" rather than William or Bill.
Edit: Should also note how ironic he was given a "savage Indian name", when he himself was vicious towards the Plains Indians during those conflicts.
Actually, he was named after Tecumseh because his father admired the Shawnee chief for being humane, educated and brave.
"Like all settlers in the Northwest, [Charles] Sherman found his first years in the new land filled with talk about the Indian Tecumseh. The chieftain was at once the despair and the hope of white civilians from Pittsburgh to the Mississippi River. If he should decree war the danger was appalling, for he held the tribes from the Great Lakes to the Gulf of Mexico in obedience to his call. If, however, the Indian war should begin, Tecumseh was the white man's one hope that women and children and captives would escape massacre. Stately, serene, and humane, Shooting Star was recognized by all thoughtful settlers as a statesman rather than a savage. He could read and write, and kept a half-breed secretary, Billy Caldwell, chief of the Potawatamis, living in a cabin close to Fort Dearborn, where the Chicago River emptied into Lake Michigan. White men felt an irresistible admiration for the great chieftain who was attempting to hold his people's land by diplomacy rather than by bloodshed. And when war did come in 1812 with the redskins scalping and burning across the Northwest, legends of Tecumseh's magnanimity and mercy grew in the log cabins. He had struck up murderous tomahawks in time to spare lives, had denounced his British allies for inhumanity; and when he was killed at the Battle of the Thames in Canada, all through the United States there was genuine regret mixed with elation. To men like Charles Sherman there was nothing but shame in the reports that American soldiers, battle-crazed, had cut long strips of skin from Tecumseh's dead thighs so that they might have razor strops as souvenirs of victory.
When peace had come to the nation with the Indians' drifting farther west, Charles Sherman went back to law and success, but through his mind there still went thoughts of Tecumseh. He decided to name his next son after the red man, but when a baby boy arrived, in December, 1814, he found that his wife had already decided to name it for her brother James. The first-born had been named for her brother Charles; the second-born, a girl, had been named for herself; and the third must keep up the family tradition. Her husband must have taken private satisfaction in the thought that Mary had no more brothers. He would bide his time and wait for another boy. In February, 1816, there came a girl to be named Amelia, and on July 24, 1818, another girl, Julia Ann. Then on February 8, 1820, a boy at last, red of hair, redder of face, a fit one for the name Tecumseh, which meant Shooting Star."
Sherman: Fighting Prophet, pp. 21-22, Lloyd Lewis