I had a long career as a degreed physicist, and am now retired and doing no physics work. I’m not sure which way of identifying myself makes more sense. The question works for any profession, I think.
One way of looking at it is that I still have my education, regardless of what I’m doing now. Another way of looking at it is that I’m not acting as a physicist.
Maybe a person saying “I am a (whatever)” could be a promise of competence. If somebody gets on the intercom and asks “is there a doctor on this aircraft”, raising one’s hand obviously suggests some ability to help right this minute. Somebody who had retired from medicine 20 years earlier, and stayed completely away from the field, might not be willing to promise that, for all I know.
Perhaps this is the distinction between career as identity versus activity.
What say the dopers?
I identify as a “Retired Person”.
(Most of my career was in IT, but my last job was as a storeman.)
I bet having or not having an active malpractice insurance policy factors into the equation as well.
In your case and others in a similar situation, I bet maintaining an active interest in the field (and not necessarily having an active competence) is a factor.
I suspect that depends on exactly what the profession is - “physicist” doesn’t just refer to a degree , does it? My daughter’s HS physics teacher had a doctorate, but I’ve never heard a HS teacher referred to as a physicist or mathematician or historian , regardless of what degree they have.
Anyway, I think it probably depends on multiple factors , including whether someone can (not necessarily does) engage in that profession independently of being employed . A retired high school teacher can’t act as a teacher without an actual job , but a retired doctor or lawyer can. They would have to have a license and maybe keep up with continuing education requirements , but those can be done without being employed.
Even though I do a little bit of consulting, I call myself a retired engineer.
I have trouble nailing down something specific when someone inevitably asks “What did you do before retiring?” I was originally trained as an electrician, but as time went on I was more of a project manager, then was a facilities manager, then a construction contracts supervisor, then the COO of a construction company, then (briefly) an RV salesman, then a facilities manager again, and finally a quality control manager. I usually just say something vague like “I was in the construction arena” or “facilities management”, which usually results in a vague nod from most people. None of those things identify me, as I never thought of any of my jobs as something that defined who I was. They were just a means to a paycheck.
I recently applied to begin receiving Social Security payments and will be retiring at some point. I’m craving the day someone asks, so I can reply, “worked”. If they ask for a more specific answer, “I’d rather not get into it”.
My pre-retirement work was not interesting enough to reference, so I’m just “retired.” When someone asks what I did before, I say “a boring office job.” It wasn’t always boring, but the last few years overshadowed the rest.
I spent most of my career as a systems software engineer.
Retired these days, but I still have FreeBSD and Linux installations running on my system (in emulation), the basic Windows development environment installed, and I’m starting to play with Rust.
I think I could get back on the horse pretty quickly if I actually needed to.
I’m not really sure how I would describe myself though… it would probably depend on the context.
I’m retired from the Army and the police department. I tell people I’m unemployed. Then my wife smacks me.
I’m retired from Boeing. Boeing is a big company with hundreds of job titles. I just pick one that hasn’t been in the news lately. Due to production issues, I never worked in my job title the last 5 years I was there.
I needed to id my “work” many times when we moved here a few years ago. Almost all the people around are youngsters. So I’d say I had been a prof. of Computer Science. One advantage of stating the field it that many people nowadays “know the type” and can adjust their expectations of my behavior.
A recently retired friend of mine identifies as “Operations Manager at Not_Working.com.” I think I will take that up when it’s my turn.
I recall that in one of the Travis McGee books he stated his occupation as “managing my investments”.
In those days that probably seemed more impressive than it does today when everyone dabbles in the stock market … 
Here at Walking Dead Manor there are a lot of retired people who were university educators, engineers and other professionals. I get the feeling that they tend to judge you by what you did, rather than who you are. I also get the feeling that they equate 20 years in the military with being poorly educated. I do enjoy taking the stuffing out of them when necessary, but I generally just avoid most of them.
I identify myself as “Retired.” If someone asks I’ll add “Professional Piano Technician for 32 years.”
(Until my hearing started glitching in my early 50’s and I chose to quit while I was on top of my game, “leave 'em asking for more.” 20 years later I’m effectively deaf and about to get my first cochlear implant.)
I would call myself a retired software engineer rather than a software engineer, even though I still do a fair amount of programming for fun, and spend a lot of time maintaining and enhancing a widely used open source product. I guess to me the difference is I’m not being paid for the work I do now. But in the unlikely event that I heard “is there a software engineer on this aircraft?” I would raise my hand.
I’m a retired chess teacher (was a full-time job. 
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if someone asks what I do I say “I’m retired”. If they persist and ask what I used to do I say “I was a programmer”. Then, of course, the say “Oh, My PC is doing this funny thing…” and I have to ask “Is it an IBM? 'cause otherwise I can’t help you.”
I spent many years programming mainframe computers in various flavors of a language call RPG, which hardly anybody uses anymore. If I had to go back to it I could probably get back up to speed in a few days, but nobody needs me to do that.
These days I just identify as “Papa”.
My husband has a PhD in physics, but does not use that any more (he’s an IT geek, like me). I’ve referred to him as a “lapsed physicist” 
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Dunno what I’d say as we retire. Seems to me like a doctor or lawyer or some other recognized, somewhat discrete profession is where you’d say “I’m a retired judge”.
Saying “I’m a retired database administrator” just doesn’t have the same ring. I might say “I’m retired, I used to work in IT”. Or just “I’m retired, woohoo!”