What is the name of this kind of connector?

Board to board connector, header.

 

I think they are generally known as Dupont connectors. You can buy male and female pins and a range of plastic headers, from single pin, 2x1, 4x1, 4x2, and larger. For sizes that you can't get, use a larger one and cut it down.
You can polarise them (make them not reversible) by blocking one or more holes in the female part and omitting the corresponding pin(s) on the male part.

 

The generic term is wire-to-board. The part on the board is an unshrouded header. The part on the wire harness is a crimp-pin, pin-and-socket, or other names. AMP and Molex are huge in this market. The header usually is 0.1" pitch, with 2 mm as a close second. These are *not* interchangeable. However, headers and wire connectors are interchangeable across manufacturers as long as the pin spacing is correct. The pins usually are 0.25" square.

ak