Copyright is for literary works (such as books), visual arts works, performance works, motion pictures, musical works, and the like.
A trademark (or service mark) is used to protect a word, phrase or symbol (or combination) which identifies goods or services and distingiushes them from those goods produced or services provided by others.
You mentioned a "business logo" which sounds more like a trade mark.
In general, because a trademark is a government-granted monopoly (as you can prevent others from using it) the mark needs to be used in commerce to obtain registration; however, if you have a bona fide intent to use the mark, you can file an application for registration and supplement it once actual use is occuring. The US Patent and Trademark Office (www.uspto.gov) has some good information which may answer your questions about the tradmark process. Note that the process and be difficult ot manage for those unfamiliar with it.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]