Branda-nîn ('Border-water') was the wide river that separated Buckland from the Shire was known to the Elves as the Baranduin, meaning simply 'large brown river', in reference to its golden brown waters. The Hobbits' name for the same river is usually represented as a punning corruption of this name, into 'Brandywine'. 'Brandywine', though, is an English name, and so cannot have actually been used by the Hobbits. Instead, it's an anglicisation based on a simplified version of the actual situation.
In fact, the Hobbits' original version of the Elvish 'Baranduin' was Branda-nîn, a word meaning 'border water', because the river formed the eastern border of the Shire. Over time, this name mutated further, becoming 'Bralda-hîm', meaning 'heady ale', and it is this later name that forms the basis of the anglicised version 'Brandywine'.