Such short phrases cannot be copyrighted - the law is clear (see this
Copyright Office publication):
Under section 102 of the Copyright Act (title 17 of the U. S. Code), copyright protection extends only to “original works of authorship.” The statute states clearly that ideas and concepts cannot be protected by copyright. To be protected by copyright, a work must contain a certain minimum amount of authorship in the form of original literary, musical, pictorial, or graphic expression. Names, titles, and other short phrases do not meet these
requirements.
On the other hand, they COULD be trademarked (see the
USPTO website):
A trademark is a word, phrase, symbol or design, or a combination thereof, that identifies and distinguishes the source of the goods of one party from those of others.
However, IMHO it would be hard to defend such a trademark outside of a very specific context. For example, the phrase "3-Gun Nation" or "3GN" could be trademarked (in fact they have been, see links
HERE and
HERE), but I am very dubious that the generic term "3-Gun" could be so protected... indeed, if you read the 3-Gun Nation TM records, they specifically disclaim any ownership of the generic term "3-Gun".
If you planned to run a 3-Gun Nation-style match, and advertised it as such, but without paying whatever dues are owed to the 3GN organization, you should expect to be on the receiving end of a cease and desist letter or even a lawsuit, but I feel entirely safe using the generic term "3-Gun" to describe my matches.