What is the name of this combination of screw and rotating metal piece that locks it?
That would be the cam lock nut and cam screw fastener.

They are commonly found in DIY assembly products sold by various retailers including IKEA.  According to a recent post I've read IKEA may be looking to replace this fastener type in its products, but I haven't seen any changes yet so probably best not to hold your breath.  However, there are alternatives to this fastener such as TorpedoCSIS.