The name Uruguay comes from the Guaraní language.
The Guaraní language is originary of one of the native tribes populating what is today know as the south of brazil, paraguay, part of argentina and uruguay. It is in fact, paraguay's second official language.
Uruguay is guaraní for "river of the birds", or "river of the painted birds", or "river of the snails" depending on the interpretation. The most accepted is river of the birds. And the whole name of the country is República Oriental del Uruguay, meaning republic at the west of this river. Before the creation of the republic this chunk of land in the world was known as "Banda Oriental" (oriental band? oriental stripe? i dunno), so it was already named in reference to the river. This is why sometimes uruguayans are referred to as "orientales", which can be sometimes confusingly funny, because it's the same term used for talking about asiatic people, orientals. ...