(This post is partially inspired by a recent article by Andreas Hölzl which delves extensively into the "Riverside Hypothesis", holding that the name manju comes from the name of a river, possibly the Amur, possibly from a Proto-Tungusic form like *mamgo.)
On the 27th of November, 1619, an emissary came to Nurhaci's court from the Ligdan Khan of the Chakhar Mongols. He bore a letter that began as follows:
döčin tümen monggul-un eǰen baγatur činggis qaγan-u ǰarlaq, usun-u γurban tümen manǰu-yin eǰen kündülen gegen qaγan mendü buyu oo?
An Order from the Hero Chinggis Khan, Ruler of the Four Hundred Thousand Mongols, to Kündülen Gegen Khan, Ruler of the Thirty Thousand Manchus of the Water: Are you healthy?
Ligdan Khan opens with this greeting as a way of asserting his authority over Nurhaci. To him, this is an order (ǰarlaq) not a letter (bičig), and his authority to issue this order came from his position as heir to Chinggis Khan, as well as the numerical superiority of the Mongols over the Manchus.
But why does Ligdan Khan refer to "Manchus of the Water", and what does that mean?
Some context can be found in Nurhaci's response, in which he says that Ligdan Khan is living in the past. Those four hundred thousand Mongols that Ligdan Khan referred to were reduced to sixty thousand when the Hongwu emperor took the Yuan capital, and Ligdan Khan was not even the ruler of all of those Mongols that remained.
If the rest of Ligdan Khan's salutation is couched in terms dating back to the Yuan dynasty, then it seems likely that his use of the expression "Thirty Thousand Manchus of the Water" is also a conscious archaicism. If so, what does it refer to?
The Chinese translators of the Manju-i Yargiyan Kooli rendered this expression as 水濱三萬人, "thirty thousand people of the river banks," so from their perspective it seems the term referred to the fact that the Manchus lived along rivers. This was definitely true of the Manchus of Nurhaci's time (despite the often-repeated claim that the Jurchens were nomadic), and was probably true of the Jurchens during Yuan times. Indeed, the centrality of rivers is even baked into the Manchu origin myth.
If you recall the story, the divinely conceived boy Bukuri Yongšon floats down a river from the Long White Mountain to a ford where people come to get water. There he makes himself a throne of willow and artemesia--two plants that grow on river banks--and is discovered and made a prince of the local people.
While they might sometimes bring mythological beings down from the mountains, rivers also provide access to fish and trade routes. More than that, the rivers in Manchuria provided access to gold and iron, both of which were gathered by panning river sand.
Given the wealth that rivers bring to those who live along them, it makes sense to me that the ethnonym manju might ultimately come from a term referring to people living along rivers, though the exact etymology of the name may still be debated.
