Focusing on a US-based company as you've asked in your question, there two steps to this issue. The first involves a commercial actor getting a nuclear power system in the first place. That's certainly doable; you might need to get some licenses and go through a bunch of regulatory hoops, but there is no reason you couldn't ultimately get permission to build and operate a RTG or some other system.
Step 2 is the problem. You don't only need permission to build and have the system; you need permission to send it to, and operate in, outer space. That's where we have what some of us call a "regulatory gap" in the United States. There is no USG agency that has the legal authority to say yes to commercial nuclear operations in space. We can do USG activities, because they get permission in different ways, but none of the current agencies that regulate commercial space activities - FCC, FAA, and NOAA - have the legal authority to say yes to nuclear devices, no matter how much they might want to or how well designed the system is. This is actually one example of a broader problem; this regulatory gap also includes many other newly-contemplated space activities, such as commercial habitats.
Finally, the USG can't just look the other way; Article VI of the Outer Space Treaty requires countries to "authorize and supervise" the activities of their companies, which means the United States has to actively regulate what commercial actors do in space, at least to some degree.
So your question raises a very current and pressing issue in U.S. national space law and policy: fixing that regulatory gap. One way to do it would be to pass a law providing some USG agency with broad authority to do "mission authorization." An Obama administration report (pdf warning) suggested something along those lines. Another possibility would have been the Space Renaissance Act proposed by then-Congressperson, now NASA Administrator Bridenstine. Neither of those proposals have moved forward, and the plans of the current administration on this issue aren't yet clear.
For non-US based companies, other domestic legal systems may well have the ability to authorize nuclear activities in outer space, and there is no prohibition on something like that under international law so long as it didn't violate some other international rule, such as by interfering with the operations of other actors.
Finally, there are some NONBINDING guidelines that have been developed internationally that could be used to guide how you might operate a nuclear power source in space.
