There are several different stories that explain, or attempt to explain, how American corn whiskey became known as bourbon. Despite the differences among these accounts, there is a common thread linking them all together: Bourbon County, Kentucky.
After the American Revolution, what is today the State of Kentucky was a large territory in Virginia. Around 1780, Virginia began to divide this large Kentucky territory into smaller units. To pay respect to the French for helping the U.S. defeat England, a bunch of these divisions were named after the French, one of which being called Bourbon County after the French royal family. So, that's how Kentucky got a Bourbon County.
One explanation of American whiskey being called bourbon was simply because bourbon was invented in Bourbon County. Many related accounts expound on this idea, claiming Elijah Craig was the first to distill "bourbon" in Bourbon County that was called "Bourbon County Whiskey." The name was eventually shortened to just bourbon. The unfortunate side to this tale is that Mr. Craig never distilled in Bourbon County and there is not one single place where bourbon can accurately be said to have been invented.
Others say that the bourbon name grew from Kentucky's trade with southern cities. Whiskey was a popular export from Kentucky, and much of it was shipped down the Ohio River. The primary port in Kentucky served Bourbon County, an area where a lot of corn whiskey was being produced. However, the vast Bourbon County was subdivided into 34 smaller counties as the 19th century approached, and the region was then known as Old Bourbon County. The whiskey that was made in this Old Bourbon region was labeled "Old Bourbon Whiskey" on the barrels that were shipped down river. As time went by and more whiskey was shipped, people began to understand Old Bourbon Whiskey to be the corn-based whiskey that many had not tasted before. Eventually, "bourbon" was the name used by whiskey drinkers to distinguish it from rye.
Along those same lines, another account tells us that both Bourbon County and Kentucky earned a respected reputation for the whiskey that the early Americans made there. "Kentucky bourbon" became the popular, generic classification for the whiskey that came from that part of the county, differentiating it from Pennsylvania rye.
Still other accounts discuss how advertising gave bourbon its name. When whiskey was shipped down the Mississippi River, it was referred to as "whiskey from Bourbon," meaning Bourbon County. In 1821, it was first advertised as "bourbon whiskey," and within 20 years, bourbon was the household name for American corn whiskey.
Finally, another explanation goes like this. By 1786, bourbon was known as "Kentucky" or "Western whiskey" so people could tell it apart it from Pennsylvania and Maryland whiskey. In this same year, about, Bourbon County was created, and near this time whiskey was first floated down the Mississippi River for trade with New Orleans and St. Louis from Bourbon County. The whiskey became to be known as "bourbon" based on its point of origin.
Well it seems that no two stories are the same. But despite the nuances, the common thread of Bourbon County remains. The most plausible explanation appears to be that many different distillers in and around Bourbon County made whiskey from corn. Since there was a concentration of these whiskey makers in the area, their corn product became associated with the Bourbon County region. Whether by trade, advertising, or word-of-mouth, this Bourbon County whiskey became popular, and eventually became known as bourbon. So, Scotch comes from Scotland, Irish whisky comes from Ireland, and at one point, corn whiskey came from Bourbon County and the surrounding area.