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...

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The 3Dcheapskate (also available in DAZ and HiveWire3D flavours) 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.