According to various newspaper articles, it seems that the town of Kilvert got it's name in 1875 and was named for Samuel W. Kilvert of Chillicothe who was (in some way) an official of one of the railroads that went through that area.
From the Athens Messenger (Athens, Ohio): August, 26th, 1875 "At the point where the Federal Creek Valley railroad will form a junction with the M. & C. (old line) there has already sprung up a respectable nucleus of the full grown town that is to be, after things get actively working. The embryo city has been christened 'Kilvert' in honor of a well known railroad official' and already includes in its structural features a new hotel building and a commercial house. The new town has taken root on a most charming and eligible site, and we feel safe in predicting that when the completion of the F.C.V.R.R., shall make things lively in that locality, 'Kilvert' will not be slow in taking material rank among the more important towns of the valley."
May 18, 1876 "The firm of Wm. Hedges ^ Son, of Big Run, we neglected sooner to mention, have sold out their mercantile business at that place. Mr. H. sr., will, we are told, shortly remove to one of his farms in that township, and his worthy son, Silas, who has recently been elected a Justice of the Peace, will take up his residence in the new and promising town of Kilvert at the junction of the Federal Creek and M.&C., railroads, where his time, when not employed in the dispensation of justice, will be directed to furthering the growing interests of the eligibly located town, above named, and of which himself and father are the founders" ."
July 17, 1876 "S.W.Kilvert, Esq., of Chillicothe, from whom the thriving village of Kilvert in Bern township, derives its hame, passed through Athens on Tuesday."