All you really need to be a "gunsmith" is an FFL and a sign that says "Gunsmith". Insurance, business license, tax ID, those are all nice to have, but there have been many gunsmiths who have appeared that had none of those. Much like knifemaking, there are industry organizations that offer training, but there is no formal, required certification process. I can become a "master gunsmith" simply by declaring myself to be so.
Reputation (good or bad) counts for some, but you get a reputation by working on guns. Most reputable smiths start out in trade school, an apprenticeship, or working with an experienced smith. When they relocate or start up their own place, they take their reputation with them. If they are any good, they might take a few customers along as well. Many are trained tradesmen (machinists, tool and die makers, mechanics, etc), and fixing guns is just more to their liking so they move into it, or they transition by using their previous skill in a gun shop. And of course, some feel that apprenticeship and training are a waste of time, because they fixed their Uncle Bill's rifle once, and it kinda works OK some of the time, even though it does have that grinder mark across the side where they slipped.
If you are looking for a smith, ask around, people will recommend someone they have used before, hopefully with good results.