There are many rivers up and down the country called 'River River' (Rother, Trent, Avon, Piddle, Thame etc.).

It's because Roman invaders asked the locals 'what's this called' and they'd say, in their own language 'river'. So the invader would say 'Ah, the river Rother' which stuck. Avon is the English way of saying Afon, which is Welsh for river. Caernarvon Castle is 'castle on the river castle'.

LTS