Let me give you a little background on what you need to do to sell in the USA. In general you want to register the trademark. That's no big deal.
The product plugs into the wall, so in many locales,in order to make it legal, you have to get the product blessed by an Internationally recognized safety agency. In North America there are 3 of them. UL, CSA and ETL. That means UL or ETL listed status in the USA, CSA or UL in Canada. If you don't have that, it is a huge liability problem. As a device which utilizes High voltage, in order to manage the product liabliity issues, you have to achieve UL, CSA or ETL listed status. That is a major pain. For example your AC adapter has to survive (and not leak) when 1200V is applied to the power cord (Hi-POT test, and failures are often spectacular)
Since the device uses electronics, you have to go out on an FCC certified test range, and verify conformance as an Class A (Commercial Device), or Class B (residential device) standards for conducted and/or radiated emissions.
This is more of a problem then it seems, since most of HID applications in the power class are automotive, and they are exempt from the standards. So a ballast/igniter that works just fine in a vehicle, may require substantial re-engineerig in a non-automotive application.
In general you also do a patent search and a trademark search to make sure you aren't going to run into problems. The classic one is that you don't control one of the trademarks you are using in the country you are trying to export too.
Having been through the exercise with several products that were UL listed, UL recognized, or ETL listed, and certified as FCC class A conforming, it is an amazingly slow and painful process. If you have made some bad choices, it can go from merely slow to excruciating. If you haven't been through the process before, the first few products are downright painful. For example if the Ballast is a UL recognized part, as long as your use is within the recognized use, that is the end of it. If it isn't, there are literally thousand of dollars in tests, and months to carry them out to make sure it meets the requisite safety requirements. Your learn real quick to try to find recognized components and use them wherever possible to prevent the agencies from spending horrendous amounts of time and your money going down those blind alleys. Even trivial things cause you trouble. We had to stop shipping some of our products with power cords, because most 240 power cords aren't UL recognized. The choice was to stop shipping them, or spend several thousand dollars getting each potential supplier approved, and product tested. Since there are about a dozen kinds of 240V plugs, the costs were absurd. Our local dealer supplied local power cords instead.
In addition, you have to agree to random inspections of the facilities, and also allow the production systems to be audited on a regular basis. Any changes in the safety critical components you use must be approved by the relevant agency. At inspection time, UL will actually verify that the parts you are using match the documentation. If the manufacturer alters the product, say updates it from 123456-A to 123456-B, you have update your documents as well, and pay UL to update their records, as well as establish that 123456-B also has listed or recognized status.
Nothing special, just time consuming and painful. ETL,CSA and UL all maintain offices in Korea to carry out the inspections and related work. We chose to use ETL at the end because they could also as a result of the same inspection, if we were careful about the documentation, could give us CE and TUV status (European conformance)
In short, this is a slow,expensive, messy and painful process. You usually hire a consultant who from previous experience knows what it is going to take to get approval, and will advise you on manufacturing techniques, parts selection, and test procedures to minimize the amount of re-work you have do to get approval status.