Well I think of myself as a designer because I went to college for Graphic Design.
I think it's common for people (especially interviewing and hiring) to assume that anybody that touches code (even front-end code) has a Computer Science background and understands algorithms and information science theory. Instead I had classes in colour perception, layout, typography, and stuff like that :D
Though wearing the 'Designer' title is easy for me because of my education, for a long while calling myself a 'Developer' felt kind of wrong, even though I was building websites from scratch and doing 100% of the work. I still don't consider myself 'Full Stack' even though I've done the whole stack before, because I only specialize in the frontend.
It's taken me about 3 years of deliberate JavaScript learning and practice before I feel comfortable saying I'm 'programming', but even though I can 100% accept the 'Developer' title now and feel confident about it, I still don't feel like a 'Programmer' yet!
Titles like this are a funny thing :D