So are you saying someone painted an Oliver to look like a Cockshutt? The Olivers and Cockshutts of that era were built on the same assembly line - the only difference is the paint and brand decals/identification. So if you have a serial number, it should be pretty straightforward to look it up on any of the Oliver or White databases.
I've always been interested by how these companies all came together. White Motor Company (trucks) bought Oliver (1960) and then Cockshutt (1962). And then Minneapolis Moline. Similar to how GM did things, you could buy the same tractor under different brand names/colors during that time. They then folded all the brands under the White brand in the mid-70's.