Despite Kentucky's prominence as a U.S. state, there are no incorporated cities or towns named "Kentucky" in either the United States or Europe.
The name "Kentucky" derives from Native American languages (likely Iroquoian "Ken-tah-ten," meaning "land of tomorrow" or similar). It was applied to the territory and later the state (admitted 1792), but unlike some state names (e.g., Virginia, Georgia, Washington), it was not widely adopted for municipalities.
While no cities bear the name, you'll find:
European place names rarely mirror U.S. state names unless directly named after them (e.g., "New Kentucky" settlements by American emigrants, which are extremely rare).