I read that as something she never did before that point. Kincaid isn't the sort of taciturn badass to let a reaction like that slip unless it was a surprise, IMO. And to my mind the thing wrong there is that Harry has just opened Ivy up to all sorts of vulnerabilities and Kincaid realises it instantly.
Kincaid wasn't present when he named her "Ivy." Harry locked him out of the apartment. Harry didn't call her "Ivy" in front of him until later. He only sees her petting Mister. The text (Death Masks, page 101 on Nook):
Hell's bells. It was adorable. She was just a kid.
A kid who knew more than any mortal alive. A kid with a scary amount of magical power. A kid who would kill me if I didn't show up to the duel. But still a kid.
I glanced up at Kincaid, who stood frowning down at Ivy fawning all over Mister. He shook his head and muttered, "Now, that's just creepy."
She went from all business, "Your life is forfeit unless you adhere to these rules"-type behavior to nuzzling a cat in the blink of an eye. Recognizing the source of the childish delight as a being who Harry later says could take one of the Ladies in a fight is creepy in and of itself.
Kincaid wasn't recognizing that there was a sudden shift in Ivy's personality, it's that he was reminded that she's a child, and his approach appears to have been to treat her as the Archive. This is a humanizing moment that came out of nowhere, for both Harry and Kincaid.
I acknowledge that names have power in the setting, and I'll admit that Ivy beginning to think of herself as "Ivy" may open her up to magical assault by using that name, but I think it's significantly different giving a mortal—Ivy
is a mortal, just with the Archive in her head—a nickname than it is to give something like Uriel a nickname. I don't think that calling her "Ivy," especially when it's done so casually, can possibly have altered Ivy within a ten-minute time frame.
There is an argument that her forming an identity around the concept of "Ivy" changed her—over the course of several years, as she naturally matured—but I think it's stretching the lore of the Dresden Files to say that Harry giving her a nickname made her suddenly like petting cats.
That is my reading of the situation; beyond that, I'll agree to disagree on this.