Yeah, and he didn't dwell on the issue. He just called her "Ayase" in the fight, and kept going. He's more insistent out of the fight though.
Also, he met her at the pool party, and had plenty of time to get a good sense of how she looks. She wears no mask. *shrugs*
See, this is where the Dub name of "Soul Reaper" would totally fix this problem, instead of "Death God".
As well, there seems to be a noted difference between "spirits" and "gods", at least in some sense. That said, I'm not terribly familiar with Eastern belief systems.
Can we just assume Kaito means he thinks they're only "spirits", and not the notably more powerful "gods"?
And Kaito's attempting to engage the wisdom and knowledge he has via carefully crafted questions.
Or is he really supposed to just sit down, shut up, and nod his head, accepting everything he's being told as 100% truth that brooks no questions or disagreement?