I have added full support of element mapping to Part WB. In addition, pure python feature now should be able to get full benefit of stable names without any code change. I have tested some python feature in Part WB. Unfortunately, PartDesign mostly use c++, and never really use Part::TopoShape, but instead, access OCCT TopoDS_Shape directly, which means lots of code changes awaiting. I still need to do some more tests before release a new version. PartDesign will definitely have to wait for the next release. Here is a sneak peek.
As you can see, after fusion the element got some funny looking names. I didn't turn on hashing, so you are seeing the raw names. After refine, the fillet edge index changed from 9 to 5, but the fillet stays the same. The refined top face got a really long names. I'll post naming algorithm in my wiki page later.
I then turned on the hasher. The name became manageable. Mind you that once hasher setting is changed, all element names of all geometry objects in the document must be regenerated, hence the recompute. But, as you can see, the fillet still remains correct.
Finally, I added another cylinder, and the edge geometrically changed. The fillet is officially broken. But, fear not, once you double click the fillet, it can magically suggest you the correct edge. So you know that I can deduce the related edges, but choose not to do it automatically. Because I think it is better to be explicit here, like many other fancy CAD do. Maybe that'll make FreeCAD feel 'expensive', too.
PS. I've modified tree view to auto expand and show you any items that failed during a recompute, so you'll know exactly what to fix.