How do I know if something is copyrighted, such as a name or word? What should I know about copyright law?

As the other answers already noted, neither names nor words can be copyrighted. A copyright protects art displays, performances and written works (this extends to modern technology such as websites, illustrations, television and film).

Copyright in Vietnam 

The protection of words, marks and names is done with registered trademarks. Just like the official copyright symbol is a “C” inside a circle, the registered trademark symbol is the letter “R” inside of a circle. The TM for trademark and SM for service mark are not recognized by the patent trademarks and copyright office. Some states may recognize them, but they are the weakest form of protection.

You should also know that you are not prohibited from using trademark names in your own works, but you must not represent yourself as the trademark holder or imply that your product is the trademarked product. This is why restaurants are so quick to note that they serve Coke or Pepsi products if you order a brand name drink which they do not serve. (As an ironic aside. The concession for Hartsfield Atlanta Airport is held by PepsiCo, in Coca-Cola’s home city.)

There is a lot more to know about trademarks and copyrights. If you are a graphic artist, the handbooks from the American Institute of Graphic Arts (AIGA) and the Graphic Artists Guild (GAG) are excellent references on this topic. I’m certain there are similar resources for writers, other artists and businesses. My advice is to find a good reference and to read it very very carefully and after you have read the basics, if there is anything that you don’t understand or that still puzzles you about your project, consult an intellectual property attorney before you make a very costly mistake.