The trouble is that larger rivers are likely to be referred to more often than smaller rivers, and you want the more-often-used concepts to get shorter names. Connecting river names is still good, but I think "the White Nile and the Blue Nile join to form the Nile" is a better way to do it.
I just read this in the Wikipedia article on the Mattaponi River and it really tickled me. If only all language were so rational!