According to Robert Rennick's Kentucky Place Names, Mrs. John Fenley named the town of Crittenden after Kentucky's Civil War Senator, 16th Governor, and two time Attorney General of the US, John J. Crittenden.  You can read more about Crittenden at the Smithsonian's site, here, or a slightly longer biography here.

Crittenden was first settled in 1812 by Louis Myers, and was earlier called Pin Hook, until 1834 when Mrs. Finley changed the name.