When my younger sister and I were primary school age, we used to say that we learned violin (and later piano) and played recorder. I think we started saying that even when we still had recorder lessons (as part of a Kodaly group class).
I actually can't remember when I would have started thinking of / calling myself a violinist. I stopped lessons in my last year at school age 16, but then spent many more years in weekly youth orchestra rehearsals so it remained a constant in my life. Younger sister pursued violin professionally and had been demonstrably much better than me since about the age of 10, so that meant I always had a very realistic view of what I was not!
Now I'm teaching I'm looking back on my teenage self with new eyes and a different understanding of what I had actually achieved at that point!
Do I call myself a pianist? Well, I certainly would say I can play the piano, but haven't practised much beyond a bit of straightforward accompanying here and there, and definitely can't play as I once could (grade 8 + on a good day with a following wind ...). And now I have a son whose abilities help circumscribe what I am not!