Name
The Surah has been titled after the word al-kauthar occurring in the first verse.

Period of Revelation
Ibn Marduyah has cited Hadrat Abdullah bin Abbas, Hadrat Abdullah bin az-Zubair and Hadrat Aishah as saying that this Surah is Makki. Kalbi and Muqatil also regard it as Makki, and the same is the view held by the majority of commentators. But Hadrat Hasan Al-Basri, Ikrimah, Mujahid and Qatadah regard it as Madani. Imam Al-Suyuti in Al-Itqan has confirmed this same view, and Imam Al-Nawawi in his commentary of the Sahih of Muslim has also preferred the same. The reason for this assumption is the tradition which traditionists of the rank of Imam Ahmad, Muslim, Abu Da'ud, Al Nasa'i, Ibn Abi Shaibah, Ibn al-Mundhir, Ibn Marduyah, Baihaqi and others have related from Hadrat Anas bin Malik, saying: "The Holy Prophet was among us. In the meantime he dozed; then he raised his head, smiling, according to some traditions, the people asked what for he was smiling, according to others, he himself told them that a Surah had just been revealed to him. Then, with 'Bismillah ir-Rahman ir-Rahim', he recited Surah Al-Kauthar; then he asked the people whether they knew what Kauthar was. When they said that Allah and his Messenger had the best knowledge, he said: 'It is a river which my Lord has granted me in Paradise.'" (The details follow under "Kauthar "). The basis of the reasoning from this tradition for this Surah being Madani is that Hadrat Anas belonged to Madinah, and his saying that this Surah was revealed in his presence is a proof that it was Madani.

However, in the first place, Hadrat Anas, Imam Ahmad, Bukhari, Muslim, Abu Da'ud, Tirmidhi and Ibn Jarir have related the traditions which say that this river of Paradise (Al-Kauthar) had been shown to the Holy Prophet (upon whom be peace) on the occasion of the mi'raj (ascension) and everyone knows that mi'raj had taken place at Makkah before the hijrah. Secondly, when, during the mi'raj, the Holy Prophet had not only been informed of this gift of Allah Almighty but also shown it, there was no reason why Surah Al-Kauthar should have been revealed in Madinah to give him the good news of it. Thirdly, if in an assembly of the Companions the Holy Prophet himself had given the news of the revelation of Surah Al-Kauthar which Hadrat Anas has mentioned in his tradition, and it meant that that Surah had been revealed for the first time then, it was not possible that well-informed Companions like Hadrat Aishah, Hadrat Abdullah bin Abbas and Hadrat Abdullah bin Zubair should have declared this Surah to be a Makki revelation and most of the commentators also should have regarded it as Makki. If the matter is considered carefully, there appears to be a flaw in the tradition from Hadrat Anas in that it does not say what was the subject under discussion in the assembly in which the Holy Prophet gave the news about Surah Al-Kauthar. It is possible that at that time, the Holy Prophet was explaining something and in that time, he was informed by revelation that that point was further explained by Surah Al-Kauthar, and he mentioned the same thing, saying that that Surah was revealed to him just then. Such incidents did take place on several occasions, on the basis of which the commentators have opined about certain verses that they were revealed twice. This second revelation, in fact, meant that the verse had been revealed earlier, but on some later occasion the Holy Prophet's attention was invited to it by revelation for the second time. In such traditions, the mention of the revelation of a certain verse is not enough to decide whether it was revealed in Makkah or Madinah, and when precisely it was revealed.

Had this tradition of Hadrat Anas not been there to cause doubt, the whole content of the Surah Al-Kauthar by itself bears evidence that it was revealed in Makkah, and in the period when the Holy Prophet was going through extremely discouraging conditions.