The Prophet ﷺ said: “Faith has some sixty or seventy branches, and modesty is a branch of faith” (al-Bukhari 9; Muslim 35), and: “Modesty brings nothing but good” (al-Bukhari 6117). The Quran describes one of the two daughters of the old man of Madyan coming to Musa “walking with modesty” (ʿala stihyaʾ, 28:25).
Meaning of the name Haya
Hayaʾ is modesty, the inner restraint that keeps one from what is shameful and urges one to do good. The word belongs to the root ḥ-y-y of life (ḥayat); Ibn al-Qayyim explains that modesty is in proportion to the life of the heart. In Turkey (haya) and South Asia, Haya is understood in this sense. In the Gulf and Jordan, Haya (هيا, with a soft h) is a different name, old in Najd, whose meaning is not established; it is often linked to the interjection hayya, “come on!”.
Then one of the two women came to him walking with shyness. She said, "Indeed, my father invites you that he may reward you for having watered for us." So when he came to him and related to him the story, he said, "Fear not. You have escaped from the wrongdoing people."