Ok, so I looked up "neuralese" but there's not much about it out there as it seems. If it's what I found (and you didn't mean the Star Trek Neuralese and their language :D), it should be some neutral / mental (and universal) language. So, if that's what it means, then I would say we don't think in "neuralese" because we don't think in any language whatsoever. It's more akin to what some "spiritual" traditions denote as "direct knowledge". I.e. a though appears and we immediately know what it means. Then several ms later a verbal commentary unfolds. Most of the time the commentary only restates what we already directly knew few moments ago, so I call it "mister obvious".

But yeah, that internal monologue adds a cognitive layer of its own. However, it's already on the level of communication. So, a rather social one.

Btw. we can observe this process also in situations outside of meditation (or other "deep dives" into psyche). E.g. when we know what we want to say, but struggle for a moment to find the word(s) to express the thought (when we say that we have it at the tip of the tongue). It's also worth noting that this voice also serves as another (although internal) input into the though-emotion feedback loop. Well, one literally talks to oneself. And I would dare to say, that the fact we are moved to create art has a lot to do with this process, too (art as communication of the verbally inexpressible).

Anyway, when it comes to identification, I prefer to disidentify with internal monologue as well as mind hence also body. After all I am that which "I" points toward, i.e. consciousness.