According to the M’nos HaLevi, Achashverosh asks two questions about the identity of the culprit to imply that wherever he is, Achashverosh would find and punish him.
R’ Meir Shapiro teaches that the word hu (“he”) implies somebody not present, whereas the word zeh (“this”) implies something present. In the context of this verse, he was asking if the perpetrator was present, or not. Incidentally, in Esther’s response in the next verse (Esther 7:6), she uses the word zeh to be clear that the Haman whom she was implicating was this one, the one right there.
Interestingly, in Purim: Season of Miracles, R’ Zechariah Fendel points out that in the phrase meehu zehv‘ai (“who is he? And where?”) the last letter of the first word (yud), the first letter of the second word (hey), the last letter of the third word (vuv), and the first letter of the fourth word (hey) spell out H-Shem’s Name.