Translated into English, República Oriental del Uruguay becomes Oriental Republic of Uruguay; The Eastern Republic of Uruguay; or the Republic of the East of the Uruguay. The last is actually the only correct literal translation, as it is named after its geographic location to the east of the Uruguay River.
Because of the ambiguity in its meaning when translated, the government of Uruguay normally uses simply Uruguay in English.
The etymology of the Uruguay River, coming from the Guaraní language, is uncertain, but the official meaning is “river of painted birds”.