How would you name and/or describe this algorithm?
I don't think there is a name for this special kind of property, but it is a clear hint for polyalphabetic substitution ciphers.
It is a special kind of polyalphabetic substitution cipher. The first alphabet is a normal random key, while each successive alphabet is generated by a one-character right shift of the previous alphabet. As a result there are as many alphabets as there are characters in the plaintext (or cipher text) alphabet.