Is there a name for this type of connection?
That is very common in what is called a shorting jack.  1/4&quot; and 1/8&quot; phone jacks often have switch contacts that are moved apart or together when the plug is inserted.  Usually the plug is breaking a connection rather than maintaining it, but it can be wired either way.
This also is common in power input jacks for something that has internal batteries plus an external wall wart power source.
Additional comment:  Plugging a pin in between separable contacts that maintains the connection between the contacts is nothing more than plugging a pin into a socket.  If the electrical relationship between the two contacts is the same with or without the pin inserted, then no switching is going on.