*The following answer relates particularly to the UK but the principle should be applicable elsewhere.*
Not all British rivers are called "River...". Yes, many of the best known ones are: River Thames, River Severn, River Mersey, River Great Ouse. However, many rivers have other prefixes or suffixes:
* Water - Blackadder Water, Ettrick Water, Water of Leith etc. (mostly Scotland)
* Burn - Bannock Burn etc. (also mostly Scotland)
* Beck - Trout Beck, Haweswater Beck etc. (mostly Cumbria)
* Gill - (also mostly Cumbria)
* Brook - Savick Brook, Dick Brook etc. (all across Britain)
* River as a suffix - East Lyn River, West Lyn River, Helford River etc.
* Creek - Barking Creek, etc.
and so on. It would be incorrect to prefix these with River: there is no such waterway as the "River Savick Brook", for example.
Consequently, it's necessary to tag those rivers which start with "River..." with the full name of the river:
river - otherwise you won't know when you can/should add "River", and when not.
name=River Thames
name=East Lyn River
name=Savick Brook