Howdy and welcome...
Well, there never was, at least not to my knowledge, a 4-door 65 GTO from the factory so that'll make it easy for people to identify your car as "not a real GTO" - if that matters to you. So, consider that before you spend lots of money on all the various emblems, trim pieces, and other visual GTO cues that you'd need. However, there's no reason at all not to give the car a "GTO spirit" like Brian (Instg8ter) has done with his Tempest by building a strong Pontiac engine/drive-train and also upgrading the suspension and brakes so that it -performs- like a GTO.
It's your car though, so it's your call.