Avraham took another wife and her name was Keturah.

-- Breshis 25:1

Classic Questions

Who was Keturah? (v. 1)

Rashi: Hagar. She was called Keturah because her deeds were as pleasant as incense (קטורת).

Chizkuni: How could Hagar be described as a person whose "deeds were as pleasant as incense" when, after Avraham sent her away, she returned to idol worship (Rashi on 21:14, above)? Clearly, she must have done teshuvah before Avraham took her for the second time, and the Torah calls her Keturah due to the sweet "aroma" of her teshuvah.

Kli Yakar: Avraham actually named her Keturah to make it known that she had done teshuvah.

Rashbam: At the literal level Keturah was not Hagar.

The Rebbe's Teachings

Hagar's Teshuvah (v. 1)

What is Rashi's proof that, at the literal level, Keturah was Hagar? (see Rashbam)

Rashi was troubled by a general question regarding the story of Avraham and Hagar. In Parshas Lech Lecha (12:5), Rashi wrote that "Avraham would convert the men, and Sarah would convert the women." From this, it follows that Hagar lived in a household where a primary focus was weaning people off idol worship and bringing them to knowledge of the One G‑d.

After living so many years in such an environment, how is it possible that Hagar, "reverted to the idols of her father's house" (Rashi to 21:14) after leaving Avraham's home? Even Yishma'el, who initially deviated from Avraham's path, eventually did teshuvah (Rashi on v. 7). Surely, then, Hagar too must have done teshuvah? But where is this fact hinted at in the Torah?

Rashi concludes that this problem can be solved at the literal level by assuming that Keturah was Hagar, a new name which she acquired indicating that she did indeed do teshuvah (see Chizkuni & Kli Yakar).

(Based on Likutei Sichos vol. 15, pp. 174ff.)