"Trey," she repeats, continuing to rub the fire-lizard's little head. "Hello Trey. My name is Kathryn."

Looking up and over at Alec, she clarifies, "Captain Kathryn Janeway," because it's okay for a fire-lizard to suddenly gain the ability to speak and call her Kathryn, but not for anyone else here. No, she doesn't allow just anyone to use anything other than her rank - especially when she's already given it out and has made the decision to not fly under the radar and pretend to be anything but Starfleet.