I'm looking for help to find a specific connector to complement a PCI Express/PCI Connector. I show it in the red circle mark. The photos are from this HAT for a RaspPi. What is the name of this type of connector?
That looks like an m3 or m2.5 broaching nut, but by the looks of it, it is not a solderable nut. It looks more like a press fit broaching nut, that is used for pressing into sheet metal or plastic. (you can tell by the corrugation on the sides which is typical of broaching nuts.)
A better way to do this is to use a solderable nut that is built for PCB's like these:
Some better options are listed here: