Well, to "obtain" a production name and trademark protection, just use it in commerce "as a trademark," generally just meaning use it in a manner that the name identifies/describes your goods and services without generically "defining" them. (If you want to register the name you can reserve it for the most part up to six months before you begin to use it in commerce)
Of course, you want to check whether others are using the same name, or other similar names, so you can try and judge whether you may be infringing on, or could be considered as infringing on someone else's trademark rights (meaning that trademark infringement is a somewhat subjective matter and even if you are not infringing it doesn't necessarily prevent you from being sued. And even if you are not sued the existence of similar marks could still affect your ideal marketing strategy).
You can contract a firm to conduct a trademark search for you. Or you can search yourself. You can search federally registered US trademarks here:
http://www.uspto.gov/ebc/index_tm.html. And of course, a trademark doesn't have to be registered to be a trademark . Other sources you can search to potentially locate trademarks include domain name directories, yellow pages, state specific trade name databases (for the most part available here -
http://www.coordinatedlegal.com/SecretaryOfState.html) and even Google. There are also several company/brand databases you could and really should try searching, notably, Reference USA, Dunn & Bradstreet, and/or perhaps most pertinently, the "Brands and Their Comapnies" database. These databases may or may not be available through your local library.
Other than this, you may benefit from registering your mark, and it is up to you to see that your trademark rights are properly enforced. A good attorney could help you with this.