Corporate Name
The rules vary on a state by state basis but, in general, each state requires that the word "corporation", "incorporated", "limited" or the abbreviations (inc., corp., ltd.) for these words must be included in the company name.  Please make sure you included one of these in your proposed name.  For example, Choice 1 might be Ajax Widgets, Inc. or Third Investment Corporation.

In addition, to the words which must be included, there are other words which may never be included in a corporate name unless permission is granted by a specific government authority such as the State Banking Department.  These phrases usually include words such as board of trade, chamber of commerce, police, bank, doctor, lawyer, trust, title, savings, mortgage and insurance.  Use of one of these words will result in your incorporation documents being rejected.

Trademark Implications
Although you may have used a certain phrase in your corporate name, it may not be enough to stop other companies from using that name in commerce and certainly not if they are located in a state other than the one in which you incorporated or qualified.  A Trademark is generally considered to be words or symbols that distinguish your products or services from those of all others.  To protect your Trademark, you must register it; in the US, with the Patent and Trademark Office.  Generally, your first step in trademark protection and registration is a search to discover any potential conflicts.  

NOTE: One of the first places to begin your trademark research is the official web site of the US Patent & Trademark Office - www.uspto.gov - where you'll find wonderful information including the ability to search the official US Trademark database.