Squish design which is on a 3d object

Am I right in thinking rhino cannily squish shapes?

I wanted to add a design to my object, I got that working nice and it shows great. I then thought I could squish the object and it will squish the design with it but it didn’t.

I’m at a standstill now, what are my options?

Provide more information and a 3dm file? As of now, there’s not much here to go on…
-wim