For me, it's when you can play something you're pretty happy with and that won't hurt others' or your own ears.
Just this morning my friend sent me recordings of me playing (a few weeks ago) on her old upright (so not a piano that would magically make me sound 10 times better
) Surprisingly, not only did I not cringe, but I actually quite enjoyed them (though of course I might be biased and should actually send other people copies and get some perspectives
). When listening to my own playing, I used to always hear the failings that made me feel like jumping off the balcony. Today for the first time, though, I actually found them decent enough that if anyone were to walk in, I would happily admit "yep that's me playing". So, I can now call myself a pianist, methinks. I'm a happy bunny