Virtues of al-Hasan and al-Husayn (may Allah be pleased with them): the hadith on the naming of al-Hasan and al-Husayn

It is narrated from Asim bin Bahdalah that he said: People were gathered with al-Hajjaj (bin Yusuf), and he brought up Sayyiduna Husayn bin Ali (may Allah be pleased with them both) and said: He was not of the progeny (offspring) of the Prophet (peace and blessings be upon him). Yahya bin Ya'mar was present there at that time, and he said: O Amir, you have lied. Al-Hajjaj said (in anger): Bring clear proof and confirmation from the Book of Allah, the Mighty and Majestic, for what you have said, or else I will kill you. He recited these verses: "And of his progeny are Dawud, Sulayman, Ayyub, Yusuf and Musa" until he reached the words of Allah, the Mighty and Majestic: "and Zakariyya, Yahya and Isa" [Surah al-An'am: 84-85]. (And he argued that) Allah, the Mighty and Majestic, has informed us that Isa (peace be upon him) is of the progeny of Adam through his mother; likewise Husayn bin Ali (may Allah be pleased with them both) is of the progeny of Muhammad (peace and blessings be upon him) through his mother. Al-Hajjaj said: You have spoken the truth, but what drove you to call me a liar in my gathering? He replied: The covenant that Allah Almighty took from the prophets, that they would make it clear to the people and never conceal it, as Allah, the Mighty and Majestic, says: "But they threw it behind their backs and exchanged it for a small price" [Surah Al Imran: 187]. The narrator said: Then al-Hajjaj exiled him to Khurasan.

It is narrated from Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) that when (Sayyidah) Fatimah gave birth to Hasan, the Messenger of Allah (peace and blessings be upon him) came and said: "Show me my son. What have you named him?" I said: I have named him "Harb." He (peace and blessings be upon him) said: "No, rather his name is Hasan." Then when Husayn was born, the Messenger of Allah (peace and blessings be upon him) came and said: "Show me, what have you named him?" I said: I have named him "Harb." He (peace and blessings be upon him) said: "No, rather his name is Husayn." Then when the third (son) was born, the Messenger of Allah (peace and blessings be upon him) came and said: "Show me my son. What have you named him?" I said: I have named him "Harb." He (peace and blessings be upon him) said: "No, rather his name is Muhassin." Then he (peace and blessings be upon him) said: "I have named them after the names of the sons of Harun (peace be upon him): Shabbar, Shabir and Mushabbir."
This hadith has a sahih (authentic) chain, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyidah Fatimah (may Allah be pleased with her) that the Messenger of Allah (peace and blessings be upon him) came to her one day and asked: "Where are my two sons?" She replied: Ali (may Allah be pleased with him) has taken them. So the Messenger of Allah (peace and blessings be upon him) set out (in search of them) and found them playing in a water trough (or the watered part of a garden), with some leftover dates in front of them. He (peace and blessings be upon him) said: "O Ali, will you not take my sons back before the heat (of the sun) grows intense?" And (the narrator) mentioned the rest of the hadith.
Muhammad bin Musa bin Mashmul al-Madani is trustworthy (thiqah); Awn and his father are also trustworthy; Umm Ja'far is the daughter of al-Qasim bin Muhammad bin Abi Bakr, and her grandmother is Asma bint Abi Bakr al-Siddiq (may Allah be pleased with them both); and all of these narrators are honourable and trustworthy.

Sayyiduna Abdullah bin Shaddad bin al-Had narrates from his father that the Messenger of Allah (peace and blessings be upon him) came out to us carrying one of his two sons, Hasan or Husayn. The Messenger of Allah (peace and blessings be upon him) stepped forward and placed him by his right foot, then the Messenger of Allah (peace and blessings be upon him) made a prostration (in the prayer) which he prolonged greatly. My father said: I raised my head from among the people and saw the Messenger of Allah (peace and blessings be upon him) in prostration, with the boy riding on his back, so I went back into prostration. When the Messenger of Allah (peace and blessings be upon him) finished the prayer, the people said: O Messenger of Allah (peace and blessings be upon him), in this prayer you made a prostration such as you do not (usually) make. Were you commanded with something new, or was revelation coming down to you? He (peace and blessings be upon him) said: "None of that was the case; rather, my son was riding on me, and I disliked hurrying him down before he had fulfilled his need (for play)."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.