The Naming of Independence
An old newspaper clipping from the Northern Kentucky University Archives notes that: "Independence was originally named Crewitts Creek on November 20, 1837, later to Crews Creek on December 27, 1837, to Bagby on July 6, 1838 and to Independence on October 7, 1840." The USPS web site agrees with these names and dates.
On the other hand, Rennick's Kentucky Place Names says that on November 20, 1837, the town was named Everett's Creek, by one Isaac Everett ( who also was responsible for renaming it Crews Creek).
Most writers agree that the name Independence came about as a result of Kenton County being created from, and thus achieving independence from, Campbell County (April 30, 1840).