Suyuti in al-Durr al-Manthur...
Suyuti in al-Durr al-Manthur, regarding the meaning of Kauthar, writes: "Buhkari, Ibn Jarir and Al-Hakim reported on the authority of Abu Bishr Ibn Said Ibn Jubair that Ibn Abbas (may Allah be pleased with him) said: `Al-Kauthar is abundant goodness which Allah gave the Apostle.' Abu Bishr said: I told Ibn Jubair that some people claim that it is a river (fountain) in Paradise, he said: `The fountain in Paradise is part of the abundant benevolence which He (Allah) gave him [the last Prophet] (as)' Razi's interpretation of the above-mentioned verse is more appropriate.
He held the view that what is meant by Kauthar is Fatima az-Zahra (sa). In Majma' al Bayan, Tabarsi writes regarding this subject: "It was said that Kauthar means abundant benevolence, it has also been said that it means the multiplicity of a given person; and the descendants of Fatima have enormously multiplied in a way that they will exist until the Day of Resurrection." Fakhr Razi made the following comment in his Interpretation of the Qur’an regarding this verse: "In reference to the third viewpoint which advocates the meaning of descendants to "Kauthar," some scholars say: "Since this chapter was revealed to refute the claim of an infidel who attempted to denounce the Prophet (S) for not having sons, it becomes clear that the meaning given here is that Allah gave the Prophet (S) offspring, which will be everlasting.
We must keep in mind that numerous massacres have been committed against Ahlul-Bayt, yet still the world is full of them [their progeny]; while the Umayyads have vanished save a few who are worthless.
Besides this, prominent scholars have descended from Fatima's sons, such as Al-Baqir, Al-Sadiq, Al-Kadhim, Al-Ar-Ridha’ (as), Al Nafs Al-Zakyyah and others." This explanation correlates to the following: An infidel denounced the Prophet when one of his [prophet’s] children died, and said Muhammad is now without offspring, therefore when he dies his name will die with him.