Literal translation is, as you said, "Kdo přesně jsi?". Could be used, tho a czech person would generally use "Kdo vůbec jsi?" (who are you actually?).

This translation is also accepted.

It is in a single clause, you need a pause: Vůbec, kdo jste? but the role of vůbec is then slightly different (actually, by the way).