Here's a selection showing the relevant bits of the PP2 where internal/external names are specified plus the internal*/external names for the 1st, 2nd, and 3rd copy of that prop that's loaded into the scene from the library**

{
version
    {
    number 4.01
    }
prop icyinglight:2
    {
    storageOffset 0 0.3487 0
    objFileGeom 0 0 :Runtime:Geometries:aerysoul:weaponscoll:icyinglight.obj
    }
prop icyinglight:2
    {
    name    IcyingLight

1st: icyinglight / IcyingLight

2nd: icyinglight 1 / IcyingLight 1

3rd: icyinglight 2 / IcyingLight 2

{
version
    {
    number 6
    }
prop SlicerSword:1
    {
    storageOffset 0 0.3487 0
    objFileGeom 0 0 :Runtime:Geometries:VaL_Slicer:SlicerSword.obj
    }
prop SlicerSword:1
    {
    name    SlicerSword_1

1st: SlicerSword / SlicerSword_1

2nd: SlicerSword 1 / SlicerSword_2

3rd: SlicerSword 2 / SlicerSword_3

{
version
    {
    number 5
    }
prop Persian_Sword
    {
    geomCustom 
        {
        ...
        }
    }
prop Persian_Sword
    {
    name    Persian_Sword

1st: Persian_Sword / Persian_Sword_1

2nd: Persian_Sword_1 / Persian_Sword_2

3rd: Persian_Sword_2 / Persian_Sword_3

As I hinted in the OP I can't make out any pattern or logic to it, although I'm sure there is some. If anybody can see it please let me know. Maybe I need more examples ?

*the full internal name (as obtained from PoserPython) has an additional ':1' suffix added for all instances of the icylight and SlicerSword

**using Edit >Duplicate 'whatever' to make a second copy gives slightly different results, which may confuse the issue...

---

The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident. And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU or something else.
*soon only to be available in two flavours -  DAZ and Renderosity