If I register a specific name as a trademark, will I be able to prevent its use by everyone else in the world?

No. If you own a registered trademark you can prevent others from using the same or similar trademark only for those goods and/or services you sell. For example, if you sell T-shirts using a registered trademark you have the right to prevent others from selling T-shirts using a trademark which is the same or similar to your trademark. Also, others may use your trademark to sell unrelated goods - like car tires or bottled water. You would only be protected for T-shirts.Additionally, federal trademark protection only extends to companies selling goods or services in the U.S. or between a foreign country and the U.S. Your competitors may still have the right to sell the same or similar goods or services between 2 or more foreign countries. For this reason, many companies register their trademarks internationally as well.