Here is a GEOMETRIC DRAWING created by Grant while he was an outstanding math student at the Military Academy. Take note at the bottom of the graphic where you will see signature as U.H. Grant.

As Grant packed his belongings to take with him to West Point, he decided to put his initials on his trunk. Using tacks he outlined H.U.G., which stood for his given name, Hiram Ulysses Grant. Realizing that these initials would cause him to be teased mercilessly by his classmates, he solved the problem by reversing the first two initials, giving himself the initials U.H.G. instead.

When he arrived at West Point his name became confused further. Congressman Hamer, who had always heard the boy called 'Ulysses,' secured his appointment to the Academy. He was unsure of Grant's middle name and thought it was perhaps the maiden name of his mother, or Simpson. Consequently, when Grant arrived at West Point, he found that he was required to register as Ulysses S. Grant or go home and fight the bureaucracy. He chose to enroll and register under the name the Congressman and Academy had given him, but continued to sign his name the way he had first intended, or U.H. Grant.

Later he adopted the name Ulysses S. Grant and continued to use it until his death.