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Parallax mapping shaders do this kind of computation in actual games. In the case where the entire scene is rendered this way, you might see it referred to as a "two-triangle" shader like at [1] (since there's only two 'triangles' in the usual sense to draw the scene), but I doubt that this is at all common.

[1] http://www.iquilezles.org/www/material/nvscene2008/rwwtt.pdf

i've used this in practice for a number of full screen effects... e.g. if something is volumetric and you are inside of it, it makes more sense to draw two triangles than an elaborate mesh that completely bounds the player.

It's a pixel shader. It's widely used for everything involving 3D graphics these days, as most engines require you to implement one, even if it's a trivial one.

That example (and many on shadertoy.com) is called raymarching

Ive had it referred to as a full screen quad.