Board to Wire Connector Type used between Small Display and Main PCB
Without a measurement scale in the photo, those are probably intended to mate with .025 " (0.63 mm) square posts on a 0.1" pitch. Back in the day wire wrap pins would have been the term. The easiest way to buy them nowadays is as a breakaway, single row male header in a convenient length. I've used digikey.com as the source just because the link was available, but any electronics part house should have what you need. A header using a smaller pitch will have a smaller pin, so don't try it unless you are willing to replace the female components.