The quick workflow.
Wrap a plane with a Bend Deformer around the object, just close not tight. Or what ever your animation needs. Just so you get a close cover.
Then make this editable, and apply a material set to spherical. Check that the Texture Sphere (Texture Mode) covers the whole object. Delete the UV tag. Then Tags>Generate UVW Coordinates.
“Displacement-Bake” this object, by pulling the main object in the Bake field - Source . (Potato) Use a high bit depth and resolution!
Delete the UV tag from the object with the deformer, and copy the UV Tag from the Baked object to the Deformed. Load the Displacement and set the same values (Height and Method—e.g., Intensity Centered)
Switch the object with the bake tag to invisible.
Render. The Deformed Object should look similar. This deformed and displaced object can now be animated without losing the surface information of the main object (Potato).
I have tried also stronger structures, since I do not know your object, I hope that works for your model as well.
I have attached an example file:
https://www.amazon.com/clouddrive/share/J1Bibl836yFNbnlamoEb9FXACJ4vS0ecXokfgL8UV01?ref_=cd_ph_share_link_copy
All the best