Inc or LLC or both?
Just to clear out any confusions there might be, a corporation and an LLC are different types of legal entities, and a corporation cannot be at the same time an LLC (and vice versa). Both entities have a lot in common (such as limitation of liability of owners), however each comes with its own advantages and disadvantages.
As far as names go you would typically put "Inc." in the end of the name of a corporation (but not limited to - some other variations are allowed such as "Corp", "Corporation", "Incorporated", etc.), and "LLC" in the end of a name of an LLC (other variations include "L.L.C.", "Limited Liability Company", etc.).