I hadn’t thought to check old USGS maps. From a quick look it seems that most of these reservoirs aren’t labeled on them (they’re mostly pretty small).
But I did another Overpass query and the plot thickened. There are a bunch of “Ksnoname” reservoirs in, you guessed it, Kansas, and also some “Mononame” in Missouri and a few in CO, OH, AL, GA, and OR following the same pattern. The ones in Kansas don’t appear in GNIS when I search for “Ksnoname” (I haven’t checked to see if they’ve been corrected or just removed), but the “Mononame” ones are still there, and so are the “Ohnoname” ones.