Let me introduce my skills first so you’ll know if I would be able to answer your future questions! 
- good knowledge of colorFabb filaments (reseller)
- good knowledge of desktop 3D printing (especially with Rep2)
- good knowledge of different CAD (Blender, Meshmixer, 123D Design, SketchUp, … )
As @MB3D told, the starting point seems to get a blank Fairphone case CAD model. With this you’ll be able to have an easy start without trying to modify an existing case. If you do not find this model and have some CAD abilities, it is not that difficult to modify an existing one by removing all unnecessary vertices.
Next, you’ll have to define if the customer want to get his image engraved or embossed. This won’t have any influence on the technique but I will definitively not recommend to engrave anything on the Fairphone case before you are sure of the process because the case could be a lot more fragile.
You’ll also need to get a vectorized and cleaned version of the image (Inkscape is capable but because I am on Mac, I prefer Affinity Designer).
Next step is the CAD software… If you are not comfortable with Blender, perhaps you should look to another software like SketchUp which is also free. These two software ARE NOT designed for 3D printing BUT can handle 3D models that will be printed. It is far more easy to have the manifold checks in SketchUp by adding some plugins (see Solid Inspector).
In the CAD software, it will be easy to import the blank case model and the vectorized image. Next step is to get some volume out of the image. Linear extrusion a way to get it.
After that, you’ll only have to play with your two objects so you’ll have the desired result.
My advise is make a simple test and print it first.
Contact me for any question or just to let me know how is it going