They were simply called 3d cards and go back a long way, at least 1920's. The posh name is Lenticular.
In the 70's Kodak, I think, marketed a camera that made them. Basically you take two images and cut then into tiny strips and then glue a piece of clear plastic embossed on one side with prism shapes.
They are still being produced, often appearing in kids toys, cereal packet gifts. Modern ones are a lot thinner. I presume you can get software to knock them out on your PC and just by lenticular film to stick over it. A little fiddly but you can see the alignment before you stick them down. I remember having them in kit form as a kid with pre printed images.