"must",well for the most part I think it might not occur to many if we should or not. But for instance in the case of American thermos company vrs. Aladdin the issue was that the public used the word "thermos" as a name for all types of hot or cold beverage containers. So as time went on the word "Thermos" was beginning to mean by definition "any container used to keep beverages hot or cold" instead of only exclusive to a company name.
In the case of Coka-cola who also used the trademark "coke" their are similar cases Coka-Cola vrs. Pepsi over the shapes of their bottles and the tendency of the public to call any type of soft drink/carbonated a "coke".
So its much the same when the word "church" is considered it was in ancient Greek two words used to call together an assembly or to describe the assembly called together but was not used as any type of "name" but rather an anonymous group that were assembled.
Beginning with Christianity the term Church was and still is used to denote a group of people who are followers of Christ. Some refer to themselves as "the Church" others use it in description of the building where they assemble, and co-mixtures of the same definition.
If the word Church is a noun,name of a certain entity and used as a namesake then it is used with a Capitol letter,example "(C)hurch" which is the case if we notice it is usually capitalized to denote it as being a name.
So if it is the "name" of the body or building of the assembly of the followers of Christ then for another inanity to use it, example "Church of Lucifer" it is an infringement on the rights of those who have used it for almost 2000 years as a name. If Christians permit them to use their trademark/name then it will be established by usage that it is just another common word and not a "name" associated with Christianity exclusively.