What is the name of the hardware used to build this dinner console table?
They're called table slides or extension slides.  They generally come in 2 versions - one for pedestal type tables (sometimes called equalizer slides) and one for traditionally legged tables.

As far as the design goes, you're pretty much limited to your imagination and woodworking ability. Just build it like you would any other extending table, but with the fixed table top only long enough to accommodate the hardware.