I would like to know if there is any copyright related rules to name a game studio specially for android appstore. I searched at the U.S. Copyright Office website and found many matches for same names. None of them are game studios though. Is it legal to choose one of those names if none of them are game studios? Also, what are the rules I need to know for starting a new indi game studio?
Naming any business in the United States can be a drawn-out, expensive process. Oh, and IANAL.
The very first thing, is that you are looking in the wrong place. You should be checking the trademark registry at the United States Patent and Trademark Office Website.
There are a few things to consider is the class, multiple marks can exist with the same word because you register per class. While one company can hold all of the classes for their name, it's not always likely because the fees can get up there.
But it doesn't stop there, because when you file for a trademark it is published for opposition. If someone has been using the name in commerce before you, they can have your application ended. With the international nature of business you may even face external (to the US) opposition.
The solution to this, is to get a lawyer who can work with you along the path, including looking up common-law trademarks around the country, and possible places where you may reach conflicts before registering. The USPTO offers no service (aside from the basic registered mark check) for looking up this information.
First of all, if you're talking about the name of a company you're asking about trademarks, not copyrights.
Second, as long as there aren't other companies with the same name in your industry (i.e. games), it's probably OK. I used to work at a game studio called Sucker Punch Productions; there's also a movie, an art/architecture magazine, a motorcycle dealership, a small film studio, a pickle company, an online radio station, an athletic supply company, and many more all named Sucker Punch. These businesses can all coexist and have the same name because they're all in completely different industries.