I'm pretty certain the only one who refers to her as just "Nico" is Eli.
e: shit, I have Maki referring to her that way, so there's no consistency. Anyways, just "Nico" + casual language (doesn't come across in the TL) = Eli for sure.
I can see it being Nozomi who caught them. She's probably standing there with a smirk on her face "lecturing" Nico on immoral behavior, hence Nico's "you're one to talk" comment.