The "year and make" of registration depends on the state. Some states register as "year/model" replicated, others like NY are current model year and "Composite" (or in some states "homemade"). See
SEMA Action Network (SAN) TAG_TITLE_TOOLBOX for the regulations in all US states.
Some people go to lengths and often contravene the DMV law to get a "1965 cobra" or such. At one point it was common to take a junked '65 Ford title and put the VIN on the new chassis. All of the "work arounds" are of questionable legality and in some state have caused tax assessments, seizures and other not so good things.