Dr. Muhammad Abu Laylah, professor of the Islamic Studies & Comparative Religions at Al-Azhar Univ. states: “Hawwa (Eve) is not mentioned by name in the Qur’an because the Qur’an is not a historical book and she is mentioned in the Sunnah and it is well known among the Companions and the righteous predecessors that Adam’s wife referred to in the Qur’an in several occasions is Hawwa.
Hawwa is not mentioned in the Qur’an because the Qur’an depends on the Jewish and Christian Scriptures. But Almighty Allah did not want to mention the name for a certain purpose and the Prophet (peace and blessings be upon him) said that not everything in the hand of the Jews and Christians are corrupt. They have some elements of truth and these elements are mixed and tampered with.
The Prophet (peace and blessings be upon him) told us that there is no harm to take some stories from the Jewish and Christian Scriptures if they bear nothing against the teachings of Islam.