The Reason for Eve's Creation
Adam knew the names of everything. Sometimes he talked to the angels, but they were preoccupied with worshiping Almighty Allah. Therefore, Adam felt lonely. One day he slept and when he awoke he found, near his head, a woman gazing at his face with beautiful, tender eyes. Perhaps they had the following conversation:

Adam: You were not here before I slept.

She: Yes.

He: From what...?

She: I came out of you. Allah created me while you were asleep. Do you not desire to restore me to you while you are awake?

He: Why has Allah created you?

She: To be your solace.

He: Thanks to Allah I was feeling lonely.

Eve's Name
The angels asked him her name. He replied: "Eve (Hawwa)." They asked: "Why did you call her Eve?" Adam said: "Because she was created of me, and I am a living being." (The root of the name Hawwa" means "living things.")

Adam Sees Eve
Ibn Abbas and a group of the companions of the Prophet narrated that when Iblis was sent out of Paradise and Adam was accommodated therein, Adam was alone in Paradise and did not have a partner from whom he could get tranquillity. He slept for some time and when he woke up, he saw a woman whom Allah had created from his ribs. So he asked her: "Who are you?" She replied: "A woman." He asked: "Why have you been created?" She replied: "So that you could find tranquillity in me." The angels, trying to find out the extent of his knowledge, asked him: "What is her name, 0 Adam?" He replied: "Eve." They asked: "Why was she so named?" He replied: "Because she was created from something living."

Eve's Creation
Muhammad Ibn Ishaaq and Ibn 'Abbas related that Eve was created from the shortest left rib of Adam while he was sleeping, and after a while she was clothed with flesh. That is why Allah the Exalted said: 0 Mankind! Be dutiful to your Lord, Who created you from a single person (Adam) and from him (Adam) He created his wife (Eve), and from them both He created many men and women. Surah 4: 1

Allah also said: It is He Who has created you from a single person (Adam), and (then) He created from him his wife (Eve), in order that he might enjoy the pleasure of living with her. Surah 7: 189