I did this in California a couple of times for $35 a pop, and once in Oregon, more recently, for $25. Normally you go to the county seat and establish that nobody else is using the name, then register it. In most states you will have to do a legal advertisement too, but they have forms in the registration office and local papers make this easy. Then, you go to your bank and take out a bank account with the new name, and you’re in business.
You may also need a business license, this would depend on local laws. Some areas require it, some don’t. Most don’t, actually.
If you will be running your business from your home the laws depend on the city rules, normally, zoning laws, and local licensing requirements. You could call your town hall or the chamber of commerce to ask. When I ran a home office business in Palo Alto in the early 1980s, you were not allowed to put a sign outside your house or take commercial deliveries. Otherwise, the city didn’t care.
As you look at these details, the best source of real help at an affordable cost is your local Small Business Development Center (SBDC). These are funded by federal, state, and local funds, and there are almost 1,000 of them throughout the country. They vary by state, but I know New Hampshire has an excellent program. Definitely one of the better ones.
Because SBDCs are publicly funded, they tend to offer business counseling for relatively low rates. I recommend them highly. You can find a list of SBDCs at our website.