Hi Everardo,
There are two different things you are talking about.
1. Your business structure (that would be like an LLC)
2. State or local government licenses/permits to do a particular business activity
1. Forming an LLC or other business entity has to do with taxes and liability (for example, if your business gets sued but you are an LLC, your personal assets are usually protected). You can get advice on this from tax or small business advisors. You don’t have to have this set up before you start running service calls, but you do want to look into it and make a decision before too long.
2. You’ll have to check with your local/state government to see what, if anything, they require before you open an appliance repair business. Fortunately, licensing requirements for appliance repair tend to be fairly minimal compared to other trades.