[While it's true he is a general, it's been reinforced since childhood that he's meant to be a keeper of the peace. Not a soldier. Which is why, instead of confirming Kylo's suggestion, he answers:]

I'm a Jedi.

[There's a beat as he considers, then he forces out another calming breath. Since waking up here, he really hasn't been acting much like a Jedi at all.]

Look, I want to apologize. For the attitude just now. [He's still wary of Ren, and doubts he'll apologize in return, but - ] I'm sure you're not that thrilled to be here either. But seeing as we'll be stuck here for a while, it'll be easier if we're both on the same page. So let's try this again.

[He extends a hand - a cybernetic hand, Kylo's sure to notice - to shake.]

My name's Anakin.