A mesh’s shape keys are grouped together in a set that is somewhat hidden from the user, though it can be found by exploring a mesh’s linked data from within the outliner. Normally it isn’t necessary to know the name of this key set except for when you want to use a shape key’s value to drive another property, at which point you are left to guess which key set from a list of names like “Key”, “Key.001”, “Key.002”, etc, is the one that contains the shape key you want to reference. This situation can easily be improved by automatically matching the name of the key set with the name of the mesh it is linked to.
The only problem with doing this that I can think of is the fact that multiple meshes can have the same key set linked to them, but I honestly don’t even know why this is even possible, I can’t think of any reason anyone would want to do this… If the meshes are identical, it’s basically the same as sharing mesh data, if they aren’t identical, it won’t work properly. I don’t think this is even intended… Might be something that should be looked into.