A trademark is a federal protection tool that protects your name, your slogan, your signature sound, signature trade dress color, and many other things as it relates to your business. People seek out trademark protection because they would like to enforce their rights that come with creating something and protecting it such as the inability to have someone who has the same name as yours or the very same thing you created. Trademarks do not go away, unlike copyrights. Copyrights have a limited timeline and eventually what you copyrighted will go into the public domain. This is to ensure that the ideas you create is not monopolized by you. The whole idea of this is to create stimulation.
So, the question is- Can I trademark a name that someone else is using?
The answer is it depends. The first thing you should do is consult with an intellectual property attorney in order to get a more comprehensive response. We do not know the name of your business or other businesses. We do not know the type of business you own or if it is trademarked. For example, you want to name your business Pencil. It is arbitrary if the name of your business is Pencil and you offer software services. Another example is Apple. Apple does not make apples, instead they make technology and technology solutions. To the USPTO, that is a very distinctive way to distinguish their company for technology and technology solutions. There are three things you should consider when you are thinking about whether you can trademark a name that someone else is using.
We highly recommend hiring an intellectual property attorney because intellectual property attorneys have access to more comprehensive tools than Google alone.