So I took 12 years of piano as a kid. Love playing the piano, although I only play once a week or so, and only play fun songs for an hour or two when I do play.
I do not consider myself playing the piano. I think of it more like "playing at the piano" I understand what a tough art form it is, I am not engaged in structured learning or skill-honing. I am playing. It is a piano. That's about it.
Design, to me, is like that. I have built between 20-40 websites. I love typography. I've laid out a newspaper front page. I've taken all sorts of pictures and love photography. I've even taken pictures for the covers of small regional magazines.
But I still don't call myself a designer.
I think the reason is that, as I learned to play the piano, I learned how to practice -- how to create a mental image of where I wanted my art to go and how to reach it. (Even I spend zero time doing that any more) I understand the art form. With design? Beats the heck outta me. Design is beyond my ken. I've bought all kinds of books on design, I've done many things people would consider design, yet I feel I know as little now (or less) than when I started.
So whether you call yourself a designer or not, beats me what kind of criteria you use. I'm designer in the same way I'm a piano player. It's there, I do it, and I enjoy it. But with design I just don't know enough to know if there's more to it than that, though.