If someone completes a medical degree but doesn’t work as a doctor, are they a doctor?

If someone completes an engineering degree and decides to pursue some other unrelated career, is that person an engineer doing [insert new career], or are they no longer considered an engineer?

If someone didn’t go to school for engineering but has mastered engineering (this is typically true for software engineers), is that person who is employed in the field an engineer, even if they don’t have a formal degree or certifications?

If I self-study math for years, am I mathematician? Or do I have to formally go to school to be considered a mathematician? What if I go to school and get a math degree but work in a field that doesn’t involve math, am I still a mathematician?

What makes a doctor a doctor? What makes an engineer an engineer? What makes a mathematician a mathematician? Is it having the knowledge of the field, going to school for it or being employed in the field?