It is pretty much subjective, isn't it. I've never claimed to be a professional musician, though I once was. I got paid for making music and was pretty good though I never achieved fame and fortune. I decided on a different path, to marry and settle in to a traditional family role. Maybe I could have done this with music, some of my friends did but they mostly went into radio to earn a living while still playing. Not many really hit is big in music and some who do get used and ripped off. When I think of musicians getting ripped off I always think of the guy who wrote "The Gambler". I don't remember the details but from what I do remember, he got very little from the song but the record company an Kenny Rogers made insane amounts of money off it. I know it was legal but I'll never be convinced that it was morally right, to my way of thinking.. when they started to make that kind of money off the guy's song, they should have given the writer more, a lot more. If it were me, it would have been on my mind every day and every night until I made it right.
Anyway, I became a contented amateur. I am happy with it.
Some of this reminds me of a tagline on a Far Side cartoon I once saw.... "
I only said I was a doctor, I never said I was a good doctor". One person's professional is another person's amateur and vice versa because words mean different things to different people, except for Steve of course...

.
For instance I
am a professional, just not in the field of music or recording. I am a professional exterminator. Like this question, in the OP, people call me with questions I cannot answer. Last week a lady called me with the question that I usually consider to be a "red flag". She had a problem with millipedes. However, she included "the question/comment" : "I want to know if the chemicals you use are
toxic because we have pets". I don't understand how anyone could ask that. Everything is toxic if it is overused or misused, heck water is toxic if you breathe it or even if you drink too much of it. Table salt is more toxic than most pesticides or herbicides. How in the world am I to be expected to control a pest/bug problem if I use something that is not toxic? What IS nontoxic?? Does she think I am going to bring some sort of lift device to pick her house up, crawl under the slab and remove all the millipedes by hand?? No.. it is just a matter of not thinking or perhaps ignorance, of making invalid assumptions. The same sort of thing applies to the question of "are you a professional?"
I'd say you are a professional if you charge for your work and get paid. You may not be a good professional and if you aren't, you aren't likely to get repeat customers. I know of doctors (and exterminators) who are professionals but they are not good professionals. They somehow manage to stay in business through advertising and cheaper prices but they have a poor reputation among their peers. A knife is a knife but not all knives are sharp and the dull knives are the ones most likely to cut you.
I could see a valid argument that Dr. Dre and all his "Beats" stuff is professional but so is Shure and AGK, in my opinion the latter is better. I think I read it in another thread on this forum. It was a thread about mixing for different mediums. someone (I wish I could remember who) who said that they were always willing to mix to suit a client's wishes, for a song to sound good with these or those monitors or phones, good in a car, etc... but they drew the line at mixing to sound good in Beats headphones... still, Beats phones are very popular and would have to be considered a pro consumer line, if not useful to a professional engineer. Still they are so widely used would it be folly to dismiss them? IDK. It is still completely subjective.
Anyone can say anything. If enough people believe it, it gains power if not truth. My chiropractor calls himself a doctor. His daughter works with him, she also used the title "doctor". They consider themselves to be doctors, I consider them to be chiropractors. My cardiologist and internal medicine doctor are, IMO, doctors. Barbers were once dentists... I would not want one working on my teeth but I bet they considered themselves to be professionals and maybe they were, I wasn't there.
So... IMO, if you make money doing it, you are a professional. You may or may not be a "good" professional. My wife is a CPA. She is a good CPA, she passed all 4 parts of the CPA exam on her first try, about 2% of people do that... so yeah, she is good. She is also by definition a professional accountant but she is regularly called on to fix things that other professionals have made a mess of. I have seen her, without skirting the tax law, change people from paying over 30K in income taxes a year to getting back near 20K... she is a good professional... and I am a blessed man because of her.
There is no definitive answer to the question in the OP other than if you earn money at it you can lay claim to being a pro, others may not agree and you will develop a reputation in any case. It will be good or bad. Maybe the question should be are you 'good at what you do' or 'do you just get by' or 'do you really have no clue, you just like what you are trying to do and having fun'.
You can be a professional! Buy the equipment and a business license and voila! You are a professional. At least you can lay claim to the title and the claim is valid, you may or may not be a good professional.
But, what do I know? Not much.
J