The easiest way to do this is to Google your potential name, and see if anyone else comes up locally. If they do, this might be a potential red flag.
Check with the state that you are planning on working in to make sure that the name is not already registered. Just because you cannot find it on Google, does not mean it is not already taken. People often get a name and then put it aside for the future. You do not want to have to worry about legal trouble down the road.
You always want to check the Federal Trademark office, uspto.gov, to make sure it is not registered elsewhere. Even if you register it with the state you are in, and there is no one else operating in the area with that name, your name could be in jeopardy. If a company that has rights to a federal name, that was registered before the creation of your business, decides to operate in your service area, it will be you that is forced to change your name .