"Why do you think the name church of Christ is the only one that can be used for a church?"
Actually the phrase "church of Christ" is not a name. It is a phrase that identifies to Whom the church belongs, i.e. to Jesus as the "founder." There is an old adage that says if one calls a dog's tail a leg, how many legs does he have? The answer of course is four! Just calling a tail a leg does not make it a leg! Likewise, calling a religious group by some phrase other than what the Bible calls it does not make it just another church. If the church belongs to just one entity (Christ), then calling it by something other than "Christ's" does not make it His church!
The word church means "called out." By the strictest definition any group of people who are "called out" from something might be a "church." There are parameters, however, that must be regarded and enforced. The key to it belonging to the Lord is that a group is called "out of worldliness" and "joined unto the Lord" (Acts 2:42-47); and in that text the Lord is said to "add to His body (church)" (Eph. 1:22-23; Col. 1:18).
There are other phrases that are in the New Testament that likewise identify the church as belonging to our Savior. "Church of the first-born," "church of God," "the body," et. al. Some have said that the word "Catholic" means "universal" and since the church of Christ is indeed "universal" it should be called "Catholic." "Catholic," however, identifies the scope of the church; it does not ascertain to Whom it belongs.
The same formula will work for other denominational/manmade designations. The church does not belong to the members who compose it, therefore, it cannot be called "Christian church." To call it "Nazarene" or "church of the Nazarene" again only identifies a place, not the Spiritual Entity to whom it belongs. "Presbyterian" means an "elder, bishop, shepherd, or overseer." Although the church of Christ is to be overseen by such men, it is NOT their church. The Baptist's have latched on to the name of John the Baptist, or it might be associated with what John did - baptize. (In fact, in one of the earlier Baptist Manuals by Hiscox, a phrase was removed that offended some Baptists. It was changed. The invasive phrase? "John the Immerser." Baptist scholars felt that it was too inclusive an action in burying one in baptism and it did not properly honor John as THE Baptist!)
To call Christ's church "Pentecostal" is to identify a Jewish holy day that is indeed recorded in Acts two for example; but it was the action taken by the people upon hearing Peter's sermon that they would be "added to the church" that was the key - not the DAY on which the preaching took place. Methodists are religiously conservative people. The church of the Lord is not named after a "method" for doing things. The Bible does not recognize Christ's body as being identified by a particular "method."
When I was preaching in Hamilton, Ohio, (1968-1970) we purchased a building from a religious group called "The Holy Temple." They were going to build another building and subsequently sold us their old one. That congregation of the Lord's people still meets at 1040 Azel Avenue in Hamilton. Did the denomination "Holy Temple" move the building? No. As "The Holy Temple" the people moved. The term "Holy Temple" is mentioned in the Old Testament; but it refers to a building or tabernacle, not a group of those "called out," and certainly not the Lord's church of the New Testament.
These lists and denominational names could go on and on. They would all come to the same conclusion, that the "church of Christ" is used to identify the Lord's people in a particular place or to recognize them universally. It is not their church. It is Christ's. He shed His blood and sacrificed His body (Acts 20:28) for it. It is not "My church." It is his.
- The New Life, 5/7/17
Spencer, IN
slightly edited