What would you call the polymerised sheet-like polymer arising from Fittig reaction of 1,3,5-trichlorobenzene?
Ignoring the complex challenges it would take to make such a structure, the name is rather unclever with the literature referring to it as "holey graphene". You could probably take this a step further with your hypothetical material and call it :


well-ordered holey graphene
or better yet, well-ordered monodisperse-C6-holey graphene.


with C6 alluding to the missing $\ce{C6}$ ring that would be present in perfect graphene. Materials science has very unrigid naming conventions. If you make it first, you can greatly influence the literature terms.

As far as conductivity goes, I agreed that it would likely be conductive or semi-conductive at a minimum similar to poly(9,10-anthracene diylidene).