I remember a time part way through college I reflected on the person I was in high school and didn't think I particularly liked that person. I rather expected this, as I was unhappy in high school and felt isolated. I reflected on that and thought that it was an important part of my personal growth and that I had finally "arrived".
What was rather unexpected is a few years later I would look back at my college self who had done that reflecting and think the same thing again.
I don't know if I want to pin any particular moment where I became a Real person, because I think I'd stop growing if I could say that about myself with absolute conviction. I both dread and anticipate the point a few years down the road where I look at who I am right now and think "I'm glad I'm past that".