Since importing an OBJ and saving that as a PP2 seems to set the 'prop' and 'name' fields to the same value (which is basically the name of the OBJ file, but with lots of provisos, as indicated below...), and prompted by EldritchCellar's comment on another thread...

Importing two copies of various OBJs with the specified names into PP2014 with no figure in scene gives me these results:

The_Cube 1.obj
--------------
External Name = The_Cube1 (Internal Name = The_Cube1)
External Name = The_Cube1_1 (Internal Name = The_Cube1_1)

TheCube 1.obj
-------------
External Name = TheCube1 (Internal Name = TheCube1)
External Name = TheCube1 1 (Internal Name = TheCube1 1)

TheCube.obj
-----------
External Name = TheCube (Internal Name = TheCube)
External Name = TheCube 1 (Internal Name = TheCube 1)

TheCube_1.obj
-------------
External Name = TheCube_1 (Internal Name = TheCube_1)
External Name = TheCube_2 (Internal Name = TheCube_2)

TheCube1.obj
------------
External Name = TheCube1 2 (Internal Name = TheCube1 2)
External Name = TheCube1 3 (Internal Name = TheCube1 3)

TheCube3.obj
------------
External Name = TheCube3 (Internal Name = TheCube3)
External Name = TheCube3 1 (Internal Name = TheCube3 1)

TheCube 5.obj
-------------
External Name = TheCube5 (Internal Name = TheCube5)
External Name = TheCube5 1 (Internal Name = TheCube5 1)

TheCube_7.obj
-------------
External Name = TheCube_7 (Internal Name = TheCube_7)
External Name = TheCube_8 (Internal Name = TheCube_8)

TheCube_9876.obj
----------------
External Name = TheCube_9876 (Internal Name = TheCube_9876)
External Name = TheCube_9877 (Internal Name = TheCube_9877)

The Cube With Spaces 6.obj
--------------------------
External Name = TheCubeWithSpaces6 (Internal Name = TheCubeWithSpaces6)
External Name = TheCubeWithSpaces6 1 (Internal Name = TheCubeWithSpaces6 1)

The Cube With Spaces and an _ Underscore 8.obj
----------------------------------------------
External Name = TheCubeWithSpacesandan_U (Internal Name = TheCubeWithSpacesandan_U)
External Name = TheCubeWithSpacesandan_U_1 (Internal Name = TheCubeWithSpacesandan_U_1)

TheCubeWithQuiteARatherLongInterestingName_78.obj
-------------------------------------------------
External Name = TheCubeWithQuiteARatherLongInte (Internal Name = TheCubeWithQuiteARatherLongInte)
External Name = TheCubeWithQuiteARatherLongInte 1 (Internal Name = TheCubeWithQuiteARatherLongInte 1)

TheCu_8_beWithQuiteARatherLongInterestingName.obj
-------------------------------------------------
External Name = TheCu_8_beWithQuiteARatherLongI (Internal Name = TheCu_8_beWithQuiteARatherLongI)
External Name = TheCu_8_beWithQuiteARatherLongI_1 (Internal Name = TheCu_8_beWithQuiteARatherLongI_1)

It looks as if Poser takes the OBJ filename, truncates it to 31 characters if it's longer, and removes any spaces to get what I'll call a 'baseName'. if you save the imported OBJ as a PP2 this is the text it saves as both the 'prop' and 'name' fields (I haven't thoroughly tested that, but observations to date seem to confirm this)

I'm assuming that loading multiple PP2s created this way has the same results as importing multiple OBJs this way (once again not extensively tested, but observations to date seem to confirm this)

N.B. I think that using 'Edit > Duplicate' adds an extra level of confusion...

---

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.