A design on the case does make it easier to spot - plus, if it is individual enough, it would prevent someone walking off with your case as other peple will also know who the case belongs to.
I did the duck on my banjo case with a paint called Japlac. It also did the duck on the inside of the clear plastic banjo head. The original banjo head duck lasted several years, but my more recent one strated to fake and crack after very short usage - possibly less effective surface preparation?
Standard Humbrol Enamel modellers paint is pretty effective for a general purpose case.
Quack!
GtD.