At this point its safe to say with the newest update for AOTR that the Black Sun Faction is no longer the traditional Black Sun nor is it just the Black Sun but a collection of various criminal Empires; perhaps a rebrand of the faction name is due.
My main suggestion is a rename of the Black Sun to Crimson Dawn, a continuation of Maul's Shadow Collective, lets be frank the only orginization that managed to get all the various criminal factions united under one banner was Maul's Shadow Collective later rebranded as the Crimson Dawn, its also lore accurate at this point, while Maul would be dead by this point his second in command Q'ira is still around and you could create a clone of Maul, its not out of the realms of possibility to do that as it HAS been done before in the EU granted it may be a bit of a too easy to see coming BUT really who else could unify all the crime lords under one banner Maul already did it once its easy to see a Clone of Maul doing the same if executed properly. The other name I had in mind was the Underworld but thats a bit of a catch all.
I mean the way that Black Sun now is operating in AOTR is very similar to how Maul's Shadow Collective worked.
The real question is at this point is the Black Sun just Black Sun at this point, I'm going to say no its more then just Black Sun it is a Criminal alliance of multiple factions Black Sun being one of four.
Anyway let me know your thoughts on this: I really think the name should be changed because at this point its now four factions in one and thus the best way to handle it is a re-brand to explain this coalition of Crime Lords came to be and since we are mixing the EU and Canon together we may as well use that to help explain this alternate galactic history faction.