Hmm... Do the slices have names in the Web Layer (in the Layers panel), or is each one simply labeled "Slice"? (The generic "Slice" would be typical here; handwritten names will override the automatic naming used by the Properties Inspector.)
I found this might be a small FW bug: if I export the slice (either current page or whole), the properties box will again display the full name. So it should be just because some developer had forgotten to update this text field at some point.
It works now.