You do not need to have trademarked your name in order to be entitled to exclusive registration of that business name (through your Secretary of State). However, make sure that you're talking about the use of your EXACT name, and not something that's close. If your company is Right Way Manufacturing and the "interloper" is Right Way Bed Manufacturing, the two might peaceably co-exist.
If you're thinking, though, of giving up your company name in exchange for compensation, then definitely speak to a corporate attorney in your area about the strategy you want to use. "Cease and desist" letters carry a lot more wallop when the person signing them has "Esq" after her name.
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.