In Sindarin, the name of the bridge was i Varanduiniant. i is the singular definite article "the", which causes the initial b- in Baranduin to take the lenited form v- (i.e., Varanduin); the final element iant means "bridge".
Sindarin
baranduin
place name. Brandywine, (lit.) Brown River
The Sindarin name of the Brandywine river in the Shire (LotR/210). It is a combination of baran “brown” and duin “river”, thus literally meaning “Brown River” (LotR/1138). As discussed by Tolkien at the end of Appendix F, the English name “Brandywine” is a punning alteration of the name rather than a translation, based on the similar Westron punning-form Bralda-hîm “Heady Ale”, a variation on the proper Westron form Branda-nîn.
Conceptual Development: In Lord of the Rings drafts from the 1940s, this name first appeared as N. Branduin (TI/61). In The Etymologies, it appeared in both forms Branduin and Baranduin, already with the etymology given above (Ety/BARÁN, EtyAC/DUI). At several point in the drafts, it was changed to Malevarn, but this was only a transient name (TI/66, PM/39).