The origin of the 102 River is a mistake in the initial map of Missouri’s northern border with Iowa when Missouri became a state in 1821. The northern border was supposed to be exactly 100 miles north of the confluence of the Missouri and Kansas Rivers at what became Kansas City. However, surveyors made errors in marking that area, so the border extended 10 miles farther into Iowa (which would have made what is now Clarinda, Iowa, part of Missouri).
The mistake was challenged in 1839 during the bloodless Honey War, when Missouri tried to collect taxes in northeastern Missouri for beehives it believed were in Missouri. The matter went before the Supreme Court, which ruled in Iowa’s favor.
We have maintained the name 102 River because the river crosses the border 2 miles from the 100-mile marker of the Kansas River. Skeptics have said it crossed further than 2 miles, so that could not be the reason.
However, in this 1842 Platte Country map of the Platte Purchase area, it shows that in the original Missouri, the 102 River did not cross about 2 sections (2 miles) from the erroneous 100-mile point.
The map shows the sections where the Missouri should be and then an area with no sections that belongs to Iowa..
Wikipedia has this on the naming of the river:
Through the years, writers have speculated on etymologies other than the Sullivan Line coordinates:
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Author Homer Croy who chronicled life in Nodaway County speculated that it had something to do with Mormon Trail migration of 1847 in which the river was 102 miles from its previous camp.[9] These coordinates do not fit the coordinates for Mount Pisgah (Iowa) which is less than 100 miles from the river although they would be close in relation to the distance from Hopkins to Kanesville, Iowa which was the outfitting point for the Mormon Trail. Another version of this story says that Brigham Young told his followers that the river was the 102nd they had crossed since leaving Nauvoo.
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Robert L. Ramsay who wrote etymologies for the names of many place names in Missouri speculated it was English translation for the earlier French name Rivière Cent Deux, this in turn being a corruption of the Osage Çondse, meaning ‘Upland Forest’[9] (however the traditional area of Osage control was well south of the 102 River)