Kosmodemyansky family name was constructed by joining the names of Saints Cosmas and Damian (Kosma and Demyan in Russian). Kosmodemyansky were priests of Russian Orthodox Church since 17th century. Zoya's grandfather Saint Pyotr¹ Kosmodemyansky was murdered in 1918 by militant godless for his opposition to blasphemy. There had been rumors that before his martyrdom he spoke of coming of two angels, who will try to set people in the right way, but in vain.

Zoya² was born in 1923 in the village of Osinovy Guy³, not far from the city of Tambov. Her father, Anatoly Kosmodemyansky, studied in a theological seminary, but did not graduate. He later worked as a librarian. Her mother, Lyubov Kosmodemyanskaya (maiden name Churikova), was a school teacher. In 1925 Zoya's brother Alexander was born. Like his sister, he was destined to become Hero of Soviet Union, and, like Zoya, posthumously. In 1929 the family moved to Siberia for fear of persecution. In 1930 they moved to Moscow.

¹Pyotr is the Russian form of Peter.
²Zoya is the Russian form of the Greek name Zoe, which means "life."
³Osinovy Guy just means Aspen Forest

Source: Valentina Kuchenkova, Martyrdom of village priest Pyotr Kosmodemyansky (in Russian)