What is the word for space that is in the solar system, but outside the heliopause? Wikipedia says the definition of interplanetary space is 


  the region dominated by the interplanetary medium, which extends out
  to the heliopause where the influence of the galactic environment
  starts to dominate over the magnetic field and particle flux from the
  Sun


While it defines the solar system as the region in which the sun is the primary gravitational influence


  The Sun's gravitational field is estimated to dominate the
  gravitational forces of surrounding stars out to about two light years
  (125,000 AU).


So, if the region outside the heliopause but inside the solar system isn't interplanetary space, then what is it?
There doesn't seem to be such a word. Interstellar space within the Solar System is still just interstellar space.

There doesn't seem to be a demand for the word you're looking for either. We distinguish space by its contents; the space within the heliosphere is called the interplanetary medium (it contains solar plasma, dust, etc.), while the interstellar medium comprises sparse gaseous molecules from the Local Fluff and (if you go far enough) the rest of the Local Bubble.

Whereas there are about 10 oxygen molecules per cubic centimeter in the interplanetary medium, there is only 1 oxygen molecule per cubic centimeter in the interstellar medium. Seeing that there is no clear boundary for the Milky Way (nor is there any single definition for a boundary for galaxies), the intergalactic medium just vaguely describes the medium within galaxy filaments; here, the space is so rarified that there is only 1 oxygen molecule per cubic meter.