They do name the system that gets blown up, but it's not one I've heard of before. So presumably it's like Alderaan; reasonably important and populated by "the enemy", but who's loss is not some sort of crippling blow to the Republic.
The fallout from such an act, though, would likely galvanize both the Reublic and the Empire to start preparing for war with each other. As we know the Resistance is covertly funded by the Republic, it would seem likely that we'll start to see more new fighters and capital ships find their way into the films as they proceed on from here.
Also, it would seem strange for Snoke to turn out to be Darth Plagueis, since he was, first and foremost, a Sith. Kylo are the Knights of Ren are very clearly NOT Sith, though they do use the dark side. So while there are similarities in back story, it would seem strange for Snoke to completely throw out all of the Sith traditions that would have been ingrained on him once he's in power among the First Order. Unless it turns out he's some sort of force-ghost-reincarnation who lost his memories but could eventually duplicate the original's work. Which would be lame.
And it did effectively destroy the government of the new republic
This is according to the "visual dictionary" (according to reddit posts on the subject)
Edited by clontroper5