Why is Harry S Truman's nickname Give 'em Hell Harry?

Because he fought in world war 1. Harry Truman was once quoted as saying, "I never gave anybody hell ... I just told the truth, and they thought it was hell." Harry Truman was known as a blunt, honest man. He told people exactly what he thought for better or worse. He called it like he saw it, and didn't take any "bull" or dishonesty from anybody. That combination of honesty and bluntness in a place like Washington, D.C. left a perception of a man you would "give people hell."
Harry was his first name, not his nick name.