As a Nicole, I get this. You have the Nicole description right on, and I rely on that Nicole to organize my life. However, I never was a Nikki. My mother calls me that, but I refused to answer to it at a very young age. Refused might be the wrong word. When someone called me Nikki, I didn’t understand they were talking to me. It never stuck. I imagine your and I are the same age, in 8th grade, “Darling Nikki” by Prince prompted every boy in my class to start calling me Nikki and then I refused to answer.
In the end, my high school friends called me Nikita, and I accepted it. That name felt like me. But otherwise, I’m Nicole, all the time. I think there’s a Nikki in there somewhere, but if you called me that, I’d assume you’re talking to someone else.