One test. This is the test logo:
View=straight on the face:
In the right the test logo is printed "as is" and glued along the surface. In the Left the test logo is stretched horizontally to 108 % to compensate the 8% difference between the straight horizontal diameter and diameter along the surface.
The difference is not big, but the stretched version has right proportion width/height.
When watched from aside, the readability depends radically which parts are hidden in the valleys:
Maybe you should do the same test with your logo. Then you could decide how big the logo should be. The next image shows a bigger example:
In theory you could make the apparent straight on the face image distortionless by stretching those parts which are on the slopes of the profile. The needed strethcing is remarkable; along the surface the slopes are 46,3 mm wide, horizontally they are only 28 mm wide. I didn't test it.
The actual placement of such version can be difficult. It's still not readable when seen from aside, if too much is hidden in the valleys. Surely the company who makes and assembles the logo can give some advice.
About my images: The surface look out rounded because I approximated the surface profile with an easy to draw spline to get rid of discontinuous surface curvature. Sharp bends or only circular roundings would split the surface to 21 slices which must be textured one by one. Continuous surface needed only one image placement.
This problem can be nonexistent in professional 3D programs, I have only some easy to use software.
3D extrusion in Illustrator can be used to do tests, CAD software isn't a must. But In Illustrator the surface generally is splitted to parts which need everyone an own image.