This is for me is THE centre of the speculation of where we go from the Carrock. I am not convinced that Bolg will be Azog's son. It is a unique idea within Tolkiens world. It would require more exposition, who is Mrs Azog (sounds daft but wouldn't the global audience speculate on the nature of "orc children" ) , the orcs are Morgoths corruptions of Elves and do not exist without "Morgoths strain" at work in middle earth. To square the circle is dangerous and probably unnecessary.
Bolg as the torturer in the dungeons of DG s quiet clearly tied to the Necromencer, Dol Gulder and a confrontation with Gandalf. If the story arc for Dol Gulder is still completed in TDOS how could he survive the second movie. Well he could but why and doesn't that make his arc repetitive and lacking dynamic?
It has been explicitly made clear that Azog is the 3 film villain. Once we decided to tell Azog's story we needed three films - Pippa
Azog mortally wounds Thorin/Dain kills Azog makes a good deal of sense and draws Azog's full arc out of the appendices into the real time movie.
Azog will haress the company and this will keep the tension going but he will have Beorn and later the Elves to deal with and he is the natural leader to raise Gunderbad and march on Erebor.
This leaves Beorn a drift perhaps the big surprise of BOFA at the last moment is the re appearance of a Necromencer sponsered Bolg whom then completes the book arc. This would show the power of the Sauron and show his capacity to influence events from a distance and would fill the wise with forebodings that Sauron's retreat/defeat at DG was more a withdrawal than a real defeat and avoids overt intervention in TBOFA .
As Manuel said in Fawlty Towers
i know nothing but its fun to speculate.
I would not be surprised if Azog and Bolg are not related (or at least not mentioned as being related in the movie). I do not believe PJ wants to get into the area of orcs having families (forgot where I uncovered that, maybe the docs in the EEs). Bolg may be the Necromencer's chief lieutenant in Dol Guldur (or more likely Azog is actually in line with the Necromencer; who probably healed Azog after the battle at Moria).