If you’re using world coordinates for your noise, then obviously as an object moves in global space, the noise will change. Here I’ve extracted a polygon and moved it: same shader tree that uses noise, but different noise because I’m using world coordinates.

You could keep the same noise by applying an offset equal to the translation:

Note that I’ve assumed that there’s no scaling of the noise. If there was, I’d have to multiply my offset by the same scaling.