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The primary is named after Teharonhiawako, a god of maize in the Iroquois creation myth, while the secondary is named after his evil twin brother Sawiskera. Teharonhiawako was a son of the granddaughter of the Great Spirit creation god. He become a farmer and was loved by people. Sawiskera was a skilled hunter but was jealous, cruel and destructive, and he was eventually conquered by his brother.
If Teharonhiawako is a farmer, that implies that there has to be knowledge of the seasons and the right time to sow, harvesting and rest of harvest procedures. There is some equivalent between Teharonhiawako and Oxomoco, the goddess of astrology and the calendar in Aztec mythology.
The main theme with (88611) Teharonhiawako is time computation, like transits or progressions in astrology, artificial satellite space operations, timetables, and everything related with time operations, especially when a work or some operation has to be finished before a determined time or date, like in the movies "Back to the Future" (1985), "Spy Game" (2001), Eight Below" (2006), "Vertical Limit" (2000), "Mission Impossible 2" (2000) and "Joseph: King of Dreams" (2000).