It depends:
Most of my income comes from trading or investing. I guess that makes me a 'professional speculator'. But on a month to month basis it's the dividends from my long only portfolio that pay the bills, with my more volatile trading income a nice (but erratic) bonus. So since I don't live off my trading income, am I a professional trader? Frankly, I find it hard to know when I'm trading and when I'm investing. I use the same general process for both.
If I stopped making money in my trading account, would I no longer be a professional? Nothing will have changed about what I know, and what I do.
I don't manage money for other people: so not a professional, but I used to. So I know far more about trading than most other non-professionals (This doesn't mean I am more profitable! The ability to calculate the parameter distribution of a Sharpe Ratio, or know that the day count convention in GBP is act/365f are not inherently renumerative. At best, I am less likely to do something stupid). Is an ex-pro still a pro? Except in golf you can't usually compete at a high level once you've retired as a pro-athlete, but I'm not sure that's true of trading as long as you retain any relevant mental faculties. You don't become a worse trader just because you're not being paid to do it anymore.
I like to think I have a 'professional approach'. Someone who trades with a similar level of care and attention that I do, but has never been a professional, could also have a 'professional approach'. Does having a professional approach make you a professional?
Many brokers ask questions about how many trades you have done, and how long you have traded for, in judging your suitability to trade anything exotic or get a margin account. Does this make you a professional?
Finally, if the market-data people are asking, I am definitely not professional. I'd have to pay extortionate pro data fees out of my own pockets, not the deep pockets of client.
GAT