Probably better that he didn't drop her name; it wouldn't have done him much good, and any mention of the yakuza--or 20th century Earth--is more likely to just confuse Kamina more.

"Amos! Okay, Amos. Seems to me like you've got really good hearing or something, knowing where those bugs were. You got any ideas on how we get back to the surface? I don't really have time for kicking back down here, when my team's up there!" He points up at the roof over their heads. Clearly his focus is already on the next step of this process, which is getting outta here as soon as he can.