"Riced potatoes" are one example. Mashed (riced) to look like rice, sometimes with added herbs and spices.
But potatoes mashed with a splash of whole cream/milk, some butter and salt is a wonderful experience if nothing else. Plain potatoes mashed with a fork only? I'll pass...
That's actually also the only reference to a pure potatoe variant of mashed potatoes I could find: Kartoffel-Reis or Kartoffel-Schnee (potatoe rice/ snow) in the german Wikipedia (no mentioning of something similar in the english version).
But they apparently require a special preparation to get their unique texture.
Also, I am german but have never heard of it before.
Not that common I would say.
And for sure nothing one would think of when hearing "mashed potatoes".
I have never seen a single recipe for mashed potatoes that did not call for milk, cream, or broth of some sort (not even Vegan recipes). Ever. Never seen a single cook from any country (in person or on TV/YouTube) make them without adding something like this. Along with seasoning of some sort. Bare minimum.