Just for interest's sake, here in the west side of the Isle of Wight we have the River Yar, which enters the Solent at Yarmouth. (Curiously, "Yarmouth" derives from "Eremue", "muddy estuary".) Over the east end of the Wight they have another River Yar, which joins the Solent at Bembridge.

There's another English county with two separate rivers with the same name, but I've forgotten which one -- sorry!