Second, you'll want to see if the name has been trademarked by another company by doing a full trademark search -- one that looks at state-level trademarks, company names and domain names, not just checking with the U.S. Patent and Trademark Office. You can run into trademark snags if another company is already using the name but hasn't gotten around to registering it.
Also, where you need to be careful is in researching the reputation of the old defunct business, particularly if it's it in the same industry. You want to be sure there aren't any lingering bad feelings about the business such that people would associate them with yours.
Related: How to Name -- or Re-Name -- Your Business
Related: What's In a Name?