Whenever I think of someones title, it's always their
work title as opposed to their education come to think of it. This is actually quite a head scratcher. If you wind up as an ice cream man and got your phd in physics, can you really call yourself a physicist?

On the other hand, what if you've been doing physics-related work for 20 years then decide to change careers to being a food preparer, is it fair that you can no longer call yourself a physicist? I don't see anything wrong with "I'm a physicist currently flipping burgers"
One thing I and actually a couple of friends of mine have wondered is if you stick with the title of "physicist" being someone with a phd and experience and such... what do you call someone with just a BS or MS? We can't be engineers because we certainly have no formal engineering training...