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.

Aren't those cities named after their respective rivers, though?

I could be wrong about those two (especially Los Angeles, which is shortened from a much longer name that may have been applied to the settlement before the river, or maybe both simultaneously) but in all other cases I can think of, rivers or other natural features tend to be namesakes rather than the other way around while still following that convention. Colorado, Delaware, Mississippi, Missouri, and Ohio are all named after rivers and we still use the "x River" format for those rivers.

It seems like it might be more of a convention for English speakers in the eastern vs western hemisphere to me.