Benham, IndianaBenham is an unincorporated community in Brown [Township, Ripley County, Indiana|Brown Township], Ripley [County, Indiana|Ripley County], in the U.S. state of Indiana.HistoryAn old variant name of the community was Benhams Store. A post office opened under the name Benham Store in 1866, the name was shortened to Benham in 1888, and the post office was discontinued in 1934. John Benham Jr., served as a first postmaster.