The name comes from the river. But it's a bit more complex than that. Wikipedia says:
. . . a Delaware word literally translated as "stone for your knife stream", based on the shale found along its shores. Early settlers to the region translated this into "Whetstone River".
In 1833, the Ohio General Assembly passed legislation intending to restore the original Native American names to some Ohio waterways, but mistakenly gave Whetstone River the name "Olentangy"—Delaware for "river of the red face paint"—which had actually belonged to what is now known as Big Darby Creek.
It's a Medical Center now. If they treat any stabbing victims, the history of the name and the place will probably go unnoted.