I want to install a switch which can feed either of two circuits but always at least one of them, never OFF. Does this kind of switch have a special name, and are they common?
Change-over switch?
I've used similar, e.g. sending sound to different speakers, depending on where I am in the house, also using one set of keyboard/mouse/monitor for more than one PC.
2-way switch (a.k.a. 3-way in some parts of the world). And yes, they're extremely common, most often used to control a light from two different locations.