The best way to protect a name is through trademarking, but first, I would highly recommend that you don’t worry about that until you are making substantial revenue from your business. Unless you are making waves in your industry, you don’t give people much reason to steal your name. You should be so lucky for people to care about your business (or name) that much!
It’s also worth noting that unless your name includes your personal one, someone’s probably thought of it before. Maybe not, but you might be surprised. Trying Googling it to see if anything comes up.
Registering an LLC won’t truly protect a name, and even trademarking won’t entirely protect it. It can be quite expensive to do the latter, depending on your state. If your business has not gotten off the ground, then I really wouldn’t recommend worrying about this. You first have to prove that you’ll still be in business by the time someone wants to steal it!
Here’s one of my favorite blogs about business naming.