Me - "I don't understand everything you are saying, but could I at least know your names?"
The "chief" - "Oh Kana, you didn't tell him our names?"
Kana - "Nah, I thought it would be better if you introduced yourselves, so he can directly know who he's dealing with."
The "boss" - "What do you mean by that?"
From his reaction, I'm sure he didn't like Kana's answer at all, but I think my presence forces him to answer in a calm manner without showing too much sign of annoyance.
Kana - "Absolutely nothing, I just said that for Yùichi."
Me - "Yes, excuse me if you didn't want to do it yourself, but I prefer when the people in front of me introduce themselves, so it allows me to identify you better."
Well, I don't know if this lie is believable enough, but I had to come up with an excuse if I didn't want the discussion to get too out of hand.
Although, thinking about it now, I don't think the "chief" would have really gotten angry.