I was recently given some materials about using "church" in the name "Church of Christ". Apparently, this information came from another congregation, whose minister has been known to be very determined to prove a point or very legalistic. The congregation is also the "Church of Christ". The question is using "church" instead of "body of Christ" as the Greek translation has "body" instead of "church." I understand that "church" means "body," but does this influence the fact? I guess translation from Greek to English there seems to be some misunderstanding.
First, let's briefly address the idea of "legalism." It has become popular, especially among the denominations, to condemn the idea of proving a point by the Scriptures. And really, it is not hard to understand why, when your ideas are based on subjective feelings and broad, general references to the Scriptures, you don't want those ideas examined in detail because they won't stand. See "Legalism: The Un-Sin" for an introduction to the topic and then read through the lesson "Should We be Picky?" for more details.
Many people "run" when someone starts announcing Greek definitions and detailed arguments. But Greek can be misused. So let's see if the arguments you heard match what is in the Scriptures.
"The churches of Christ greet you" (Romans 16:16). The Greek word in this verse is ekklesiai. The base word is ekklesia and the ending means the word is in its plural form and that it is the subject of the sentence. Put simply, the word ekklesia means "assembly." Some translate it literally as "the called out" as in those who have been called to gather.
"And He put all things under His feet, and gave Him to be head over all things to the church, which is His body, the fullness of Him who fills all in all" (Ephesians 1:22-23). This particular verse uses both "church" and "body" to describe the same organization, showing that they are equivalent. The Greek word for "body" is soma. It basically means the same thing as "body" in English. While the church (the called out or the assembly) and the body both can refer to the same organization established by Christ, it does not mean that the two words mean the same thing.
The multiple descriptive terms help us understand something which one word or phrase cannot fully capture. Just as I may be called a man, a father, a preacher, an elder, a Tae Kwon Do instructor, and much more; each is an accurate description of me but none fully and completely by itself captures who I am. The person wanting to call the church only "the body" is limiting himself and missing the full depth of the descriptions of Christ's body.