The question is a good one but it needs to be answered as two or three different ones. Anyone can call themselves a luthier and anyone can dedicate their lives to that. There are restrictions in some countries as soon as you start making money and have to pay business licences and taxes. I am unhappy with the term luthier because it causes some folks to demand an all-emcompassing knowledge of all stringed instruments. If that is the pre-requisite for being called a luthier I am certainly not one. I can fill all your needs in terms of spanish guitars but that is about where my knowledge ends. Obviously the term luthier is here to stay so I think we could be a little more generous in its definitions i.e. maker of any stringed instrument.
Being a professional in this day and age means earning a living at that particular job - sorry - dictionary definition. I think this is a very useful definition. If you can't make a living at your craft you (and your potential clients) need to look at whether you know what you are doing both technically and business-wise. There are plenty of ways to tell folks that you are serious without using the term professional. Last on the list is the question of Master Luthier, Maestro Artesano and King of the Universe. In Granada we have at least one of each (self-proclaimed) and one Dean of Guitar-makers who is also self-proclaimed and is neither Antonio Marín nor Manuel Bellido.
Antonio and Manuel have there heads over their workbenches and have never claimed to be anything but guitar-makers but somehow are world-renowned, excellent artisans, have over fifty years on the job and have taught or guided innumerable makers who are now among the greats. Maestro guitarreros without a doubt. Yes, you do need that sort of resume to aspire to the title of Master.
Training is a bit like the afore-mentioned rating system, it depends who is doing it. Given that you have to do an awful lot of building to get good at building I think a lot of courses fall very short of the mark. My personal opinion is that you will benefit greatly by having a teacher or a mentor who is a successful professional and when I look at great makers I often see another great maker somewhere in their past.