Kylo Ren is obsessed with Darth Vader and vows to finish what he started.
He wields a red lightsaber.
He opposes the Jedi.
He fights for the
Empire... err First Order
Does that mean he is a Sith?
In the visual dictionary for The Force Awakens, it mentions that Kylo Ren "is the archetype of a new generation of dark side users that have emerged to fill the void left by the Sith's demise." Later on, it says: "The Supreme Leader [Snoke] believes Ren to be the ideal embodiment of the Force, a focal point of both light and dark side ability." It says that Kylo Ren is the "embodiment of conflict, drawing upon contradictory teachings and deriving power from discord."
Based on the evil things he does in the film, however, and the way he uses the Force, it appears that Kylo Ren is much closer to being a Sith than a Jedi. Nevertheless, this information proves that he is a different user of the Force, neither Sith nor Jedi.
Near the end of the film,
when Rey has defeated him in their lightsaber battle, Supreme Leader Snoke orders General Hux to bring him to him so that he can complete his training.
Whatever Kylo Ren is aspiring to be, then, he isn't completely 'there' yet, and we'll probably get to see him in complete power in Episode VIII.
Found an answer myself.
According to J.J. Abrams, in an interview to Empire magazine, He is NOT a Sith (despite being a Dark Side user of the Force):
"Kylo Ren is not a Sith," confirms JJ Abrams in the new issue of Empire. "He works under Supreme Leader Snoke, who is a powerful figure on the Dark Side of the Force.”
In addition, canon Visual Dictionary explicitly says that he's not a Sith on page 24:
... His ability to use the Force grants him many impressive combat skills, but Kylo Ren is no Jedi, nor is he a Sith.
He is the archetype of a new generation of Dark Side users that have emerged to fill the void left by the Sith's demise
We don't have to go to the Expanded Universe / Legends to determine whether or not there are dark users of the force who are not Sith. Both The Clone Wars and Rebels both contain dark-force-users who are not Sith.
The Clone Wars featured Asajj Ventress and her sisterhood. While she worked alongside Dooku for much of the series, he made it abundantly clear that she was not a Sith - that there were only two Sith, himself and his master, Sideous.
Rebels features characters known as Inquisitors. These people are force-users, and definitely dark, but again, they're not Sith.
Given that there are force-using bad guys in established Canon who are not Sith, there's really no reason to believe that Kylo Ren is a member of the Sith simply because he's a bad guy who uses a lightsaber and the force. :-)
In this movie they begin to diverge from the EU by separating the dark side and the sith. Instead of all dark side users being Sith, the Sith were just one manifestation of the dark side of the force at one point in time. Yes, the Sith were behind the empire but the Sith are no more (so we think...) and now the Knights of Ren are the current manifestation of the dark side of the force.
The idea is that there are two sides of the force. The light side and the dark side and that there is a balance that must be upheld. Very Ying / Yang. The Jedi were the manifestation of the light side while the Sith were the manifestation of the dark. Both have been nearly obliterated from the universe but the force doesn't stop existing because of this and now the light side and dark side are now moving forward in new manifestations.
I will not post my "proof" as its all spoilers from the movie.
The name "Sith" has meant a number of different things over the history of Star Wars, in-universe and out. As of the time of The Force Awakens, the Sith were most recently an organization of Force-users bound by a number of traditions. Their most famous tradition was serving the Dark Side of the Force, but they were also recently famous for only having two members at a time (though this rule seems to have been honored in the breach more often than not).
At this time, Kylo Ren is not known to be a Sith. He does indeed serve the Dark Side, but the First Order is a different organization. Given his obsession with Darth Vader, it is certainly possible -perhaps even likely- that he would seek out knowledge of his grandfather's organization. He may even hope to re-found it one day, or possibly to cast the First Order as "heirs to the Sith" in some way. But if he has plans in this direction, then he does not seem to have made his move just yet.