Forgive the quirkiness of the title; I am not aware of a name for this concept, therefore I just made a few up.
This blogpost is about a particular way to construct what I call a "pseudorandom permuter". It is distinct from a regular pseudorandom number generator (PRNG) in that it is constructed such that the sequence will never repeat until all $$$M = 2^k$$$ integers in its machine-integer state space (32- or 64-bit) has been used. In other words, it's a way to produce a permutation of $$$[0, M)$$$ that's (hopefully) statistically indistinguishable from a truly random permutation.