The word 'Al-Kauthar' means the abundant good which Allah gave to him (the Prophet ﷺ Muhammad). Abu Bishr said: I said to Saʿid, "Some people claim that it (Al-Kauthar) is a river in Paradise." Saʿid replied, "The river which is in Paradise is one item of that good which Allah has bestowed upon him (Muhammad).
الْكَوْثَرُ الْخَيْرُ الْكَثِيرُ الَّذِي أَعْطَاهُ اللَّهُ إِيَّاهُ قَالَ أَبُو بِشْرٍ قُلْتُ لِسَعِيدٍ إِنَّ أُنَاسًا يَزْعُمُونَ أَنَّهُ نَهَرٌ فِي الْجَنَّةِ فَقَالَ سَعِيدٌ النَّهَرُ الَّذِي فِي الْجَنَّةِ مِنَ الْخَيْرِ الَّذِي أَعْطَاهُ اللَّهُ إِيَّاهُ