The village was first reported in 1898 by the U.S. Geological Survey as "Salchaket," an Indian name meaning "mouth of the Salcha." The village was reported in 1904 as "Saltshatsheg."
That's what I got from the Alaska Place Names Dictionary, but nothing tells me what the name Salcha means. Just that the other names are derived from it. What native language is the name from? Maybe that would help.
Jeremy, it probably evolved as the usual non-native derivation of the name, as have had most native place names around North America. No fancy science nor anthropology otherwise.
Dang, sorry. Likely Athabaskan, given this immediate area. There were several small groups of Athabaskans around the mid to upper Tanana before villages became permanent places for them to live.
Pull out a map of Alaska and see how the place names vary from the Interior to the Yukon-Kuskowim Delta regions for example; you will see how place names are associated with the native populations and their languages.
Places like Minnesota also native-language place names. Check it out.