Complex sentence: Truman had entered the Senate in January 1935 with a reputation as an errand runner and ("the senator from Pendergast") and had become well known during the war as the chairman of a Senate investigating committee.
Split into simpler sentences: Truman had entered the Senate in January 1935 with a reputation as "the senator from Pendergast". Then he had become well known during the war as the chairman of a Senate investigating committee.