Ohio, as do most states, does not require the registration of privately sold guns. When I lived in Ohio, I bought and sold many guns privately. Point in case would be The Grand American Trapshoot where people from around the world would gather in Vandalia and sell guns privately in plain view of policemen.
The only state I am aware of that requires mandatory registration is Illinois.....you must register each gun & caliber/guage owned and be issued a FOID card. From that point on if you aren't registered for that particular caliber/guage....you can't purchase ammo for it. Subsequent any sales/purchases must be reported. The only exception came with this year's relocation of the Grand American to Sparta, IL.....the state allowed firearms & ammo sales w/o a FOID or respective reporting of such to attendees.
As for firearms not being registered in people's names......they are in fact registered in a person's name when the "yellow" ATF document is completed and documented in an FFL's logbook. The book requires the gun manufacturer, model, s/n, date received into stock, date sold, and to whom sold. The yellow form is to be submitted to the ATF periodically. This yellow form is the one we all fill out if we purchase any firearm from a legitimate "dealer"- not to be confused with a private party.
