Assuming you're in the USA, doctors are licensed by their individual states. With few exceptions, any doctor can do anything. In practice, they tend to specialize and band together into associations - plastic surgeons, urologists, cardiologists, etc. The associations are the ones where most of the rule-making comes from. An independent doctor can do pretty much as he pleases, but finding one is the big problem, particularly now that there are so few independents.
I know the guys who opt for nullo surgery don't always use doctors; and I've seen some comments that some of the practitioners will do implants. It was a pretty big deal until just a few years ago, when testicle implants other than "replace one that's missing" became acceptable to most urology and plastic surgery associations. I think they finally realized how much money they were leaving on the table.
Regardless of what type of surgery you get and who you pick to do it, you need to be an informed consumer, and then have a talk with the doctor of practitioner about what he normally performs that type of work. If he doesn't want to answer, doesn't seem sure, or tries to baffle you with bullshit, go somewhere else.
For some people the idea of an unlicensed practitioner would be an absolute "oh, hell no!" On the other hand, there's the old not-joke: "Do you know what they call the guy who graduates *last* in his class in medical school? 'Doctor'."
