What is the meaning of the names of the Well of Zamzam: Taybah, Barrah, Al-Madnunah, and Zamzam?

Ibn Kathir, the Hafiz, mentioned that Abd al-Muttalib was commanded to dig Zamzam after a vision came to him in his sleep, asking him to dig "Taybah," then "Barrah," then "Al-Madnunah," and finally "Zamzam." He described it as a well that never runs dry, never shrinks, and provides drink for pilgrims. Its location was described as being between the dung and the blood, at the spot where a piebald raven pecks, and near an anthill.

Imam al-Nawawi explained that the reason for its naming as Zamzam is due to the abundance of its water, or because Hagar contained its water when it burst forth, or due to Jibril's humming (zamzamah) and speech. He also mentioned that it might not be derived from any root.

It was also said: It was named "Taybah" (Good) because it is the opposite of impure, and "Barrah" (Virtuous) due to its many benefits and abundant water, and "Al-Madnunah" (The Cherished) because it is guarded due to its preciousness.