The horseman was Turner Ashby, who was usually just referred to as "Ashby." His war horse was named "Tom Telegraph."
On April 17, 1862, a Union cavalry charge against Ashby and a small number of his men led to hand-to-hand fighting. In the midst of the skirmish Tom was shot in the flanks but still managed, while bleeding profusely, to jump two fences before falling to the ground. Ashby paused briefly to pet the horse's mane. "Thus," an eyewitness wrote, "the most splendid horseman I ever knew lost the most beautiful war horse I ever saw."
Edit - There may have been some or even many people who referred to Ashby simply by his last name, but I wouldn't consider that to be a nickname. He had at least two nicknames.
Hoosier