I found this in the book 1001 Kansas Place Names at the Hays Public Library:

Plainville (Rooks)
The name is descriptive of the high plains area where it is located. Judge Darland had suggested the name Plainville to town planners.
PO: April 10, 1878-; Pop. 2,458

A more detailed accounting of the naming of Plainville is available on the Rooks County Economic Development Commission:

The north half of the original townsite of Plainville was first settled upon by Mr. Washington Irving Griffin, July 1, 1876. Mr. Griffin, from Pennsylvania, and his wife, Lydia R. Griffin, settled near what is now the east corner of Washington and Mill Streets. Mrs. Griffin was the first lady resident of the town and, for some time, was the only woman on the prairie between the Solomon and the Saline Rivers.

In May 1878, the Plainville post office was established with Mr. Griffin as postmaster. He soon started a store, which was then the only trading point between Stockton and Hays City, a distance of 45 miles. The name "Plainville" was arrived at when Mr. Griffin went to the homestead of Lambert P. Darland to fix up the papers to start the new town. Mr. Darland suggested the name Plainville, and without questioning, Mr. Griffin, on whose farm the town was to be started, agreed, and Plainville it was.