Legal Question in Constitutional Law in Ohio

You may be confusing copyrights with trademarks. "Baptist" cannot be copyrighted. Trademarks are another matter -- it all depends on how it is used.

Generally speaking, a Baptist church would not be able to trademark "Baptist," but may be able to trademark a mark using "Baptist" in it (such as "THOMAS ROAD BAPTIST CHURCH"). But that would not prevent another Baptist church from using "Baptist" in its name unless it was confusingly similar, like "THOMAS STREET BAPTIST CHURCH" in the same community.

Generally speaking, if "Baptist" is descriptive (as in, you would not use "Baptist" in the name of a Catholic church), then i cannot be trademarked even though it can be used in a trademark. But if "BAPTIST" is being used as a mark for something other than describing the religious denomination (such as using "BAPTIST" as the brand name for potato chips or mechanic tools), then it could be trademarked.