We don't know, as of the current canon.
The only meaningful evidence comes from his enemies, in that, really, whatever-Ren-is, and the Sith, are pretty much the same thing in different brush strokes:
The only fight: against the dark side.
Through the ages, I've seen evil take many forms.
The Sith. The Empire. Today, it is the First Order.
Their shadow is spreading across the galaxy. We must face them. Fight them. All of us.
Neither J.J. Abrams, or Visual Dictionary, nor novelization, offer any meaningful details on what distinguishes these guys from Sith except for their abilities (see below), other than confirming that they aren't Sith.
Having said that, I really don't see why he'd want to be a Sith instead of what he is.
Remember: this is a half-trained acolite (Snoke tells Hux to fetch him from StarKiller after he's injured, because it's time to finish training him):
Leave the base at once and come to me with Kylo Ren.
It is time to complete his training.
And yet he can:
Neither Vader nor even Sidious could do those things, so whatever Snoke is training Kylo Ren to be, it appears to be a more powerful and thus appealing shade of the Dark Side.
So far, the only meaningful Force Power we saw the Sith display in canon that Kylo Ren didn't do yet is shooting
bolts of lightning from his arse, Braveheart-like Force Lightning out of his hands.