Rabbi William Cohen was the son of the late Shlomo and Dvora Cohen. He graduated from Yeshiva College of Yeshiva University and its affiliated Rabbinical School, Rabbi Isaac Elchanan Theological Seminary in New York City in 1943. In 1976, they awarded him an Honorary Doctor of Divinity degree. He served as President of the Rabbinical Council of Connecticut and on the Executive Board of the Rabbinical Council of America, as well as Chairman of the West Hartford Rabbinical Council. Rabbi Cohen served for 50 years as Rabbi of Beth David Synagogue, the first Orthodox Synagogue in West Hartford. He was an ardent Zionist and Israel was always dear to his heart. For many years, he would spend half of the year in Israel and maintained a home in Jerusalem.

Rabbi Cohen served with the late Rabbi Haskel Lindenthal and Rabbi Abraham AvRutick on the first Hartford Kashrut Commission. He was one of the earliest supporters of the then named Yeshiva of Hartford and taught classes there. He was the founder of the Midrasha, the local after school Hebrew High School where he also taught. He was additionally active in the creation of the Hebrew High School of New England. Rabbi Cohen traveled to the Soviet Union in 1976, where he met with leading Refuseniks such as Natan Sharansky and Ida Nudel, and he visited Jewish communities in Hungary, Romania and Czechoslovakia.