The Uruguay River

No. The longest river in Uruguay is the Rio Negro.

Because of the river of that name that is between Uruguay and Argentina.

But that is the River Plate, or Rio de la Plata... is there even a river called 'the Uruguay', or Rio Uruguay?

The Uruguay River that borders Uruguay with Argentina.

The Uruguay River ("Río Uruguay" in Spanish) is the longest river in Uruguay. It has 1,770 kilometers (approx. 1100 miles) of length. It separates the country from its neighboring country Argentina and it's from where Uruguay takes its name.