What is the correct name of this type of switch
There is no off-the-shelf switch that performs that way.  You can achieve the same result with a momentary switch (pushbutton, toggle, whatever) controlling a small latching circuit, with a p-channel power MOSFET switching + voltage to the load, or with an n-channel power MOSFET switching the return.
OR - going old school - a momentary switch and an SCR.  Note that an SCR will have a larger voltage drop across it than a MOSFET would at the same load current.
EDIT:  There is a classic circuit with a SPST momentary switch and a DPST (or DPDT) relay, where one pole forms a latch that keeps the relay coil energized after the switch opens.  From your description, this technique will not work for your application.  You need some kind of load current sensing device/circuit/function to effectively reset the power-on latch when the load current returns to zero.