Generally, as long as no one else in your state is using that business name, you can call your company whatever you like. Names are doled out on a first-come, first-served basis. If your exact business name is taken by another company, your state's Secretary of State will not permit duplications so as to avoid confusion.
That said, you can run into trademark issues if your business and another's fall within the same category or are substantially similar. You can be found liable for trademark infringement or trademark dilution if you insist on pursuing your name without regard to how others are using it.
In particular, if you find that these "others" are large, multinational corporations then you may want to consider choosing a different name rather than risk a long, drawn-out lawsuit.
To avoid a possible fracas, you'd be well served by doing a trademark search to find out which other companies may be using in your exact (or similar) name and whether they are using it in the same way. To do this, I recommend working with an attorney to help you with the process. Otherwise, you can go to LegalZoom.com and order a "comprehensive U.S." search, assuming you're not doing business overseas.
Related: How to Name Your Business
Related: Renaming Your Business
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.