The Ganges, Nile, Danube, Seine, Volga, etc. are mostly just referred to by those names alone; for example, the Wikipedia articles for those rivers do not have the word “River” in their titles.
American rivers are mostly “X River” even when they’re not named for a place, like the Snake River or Rogue River in Oregon. (Both of which are names translated from French, and originally referred to derogatory impressions of the local Native Americans.)
Rivers in Britain and Ireland are usually “River X”, not “X River” — like the Thames, Severn, Clyde, Shannon, Liffey, or Lee. (This is the same word order used in the Gaelic languages.)
The names of oceans are adjectives: Pacific, Atlantic (“of Atlas”), Indian, Arctic (“of the Bear [constellation]”), Southern.