I wasn't planning to respond to this thread anymore, but it appears we have a fundamental misunderstanding of basic communications surrounding societal labels.
All of us use labels everyday to describe ourselves and those we come in contact with. Labels are not mutually exclusive. If someone is a "student", he/she can also be a human, a son/daughter, a brother/sister, an American, a [insert favorite band] fan, an artist, etc. We are what we consider ourselves to be. For example, an American who has been living in Europe for years and has completely integrated into a new society and gained new citizenship can still be an American (as well as a European).
Labels differ depending on each person's understanding of them, just as every word differs, even when clear-cut definitions are given. The color blue can be perceived slightly different for each person, with large overlap so that everyone mostly agrees. If you say, "I am 'x' label, and those who aren't the same as me aren't really x, even if they call themselves x," you're going to be wrong most of the time. Pop your bubble and open your eyes.
When one gains a bachelor's, master's, or doctorate in physics and decides not to continue with further formal education, one either gains a job as a physicist, switches fields, or remains unemployed. In the majority of the cases, a job that utilizes physics knowledge and skills is not going to have the specific label "physicist." Shockingly, a person with the job label "engineer" can consider him/herself to be a physicist as well as an engineer! Even more shockingly, a physics professor can be a physicist, a teacher, a mentor, a mother/father, a volunteer, an athlete, a scuba diver, and a race car driver! The band Queen's guitarist is an astrophysicist as well as a musician and rock star. Imagine that!
Tying this nicely back erotomania's original question, it almost doesn't matter what label your degree is. Almost. The knowledge and skill sets you learn in college/university and work experience, as well as the way you learn to think, contribute to your identity. Others' perceptions of your identity based on your degree label also influence what direction you head. In the big picture, you have the majority of the control over what you do and where you end up. Don't let others' ideas of what's proper hold you back from realizing that your education and career path is much wider than some would lead you to believe.