The Church of Christ denomination is much more prevalent in the southern portion of the Bible Belt, and down south if you call them a denomination...well, let's just say "Them's fightin' words!" This is one of their foundational tenets. You might be asking yourself, "What's the big deal? Who cares if they think they are a denomination or not?" The answer is that it's not a big deal, unless you know the logic behind why they make the claim. It is simply this: if they accept being called a denomination, then that would relegate them to a position within the Body of Christ. But their claim is that they are not just a part of the Body of Christ, but that they are THE BODY OF CHRIST! The sad thing is to hear what great lengths they will go to in order to shun the label of "denomination." They will actually redefine the term in such a way as to cause the unaware to agree with them. As an ex- member, I have heard so many definitions for the word "denomination" over the years that it's hard for me to remember them all. The most common one they use is that a denomination is "a group or thing that has come out from an original group or thing." Now that fits their theology just fine, thank you, because it allows them to say that all denominations are "groups that came out from the original group" which, you guessed it, the original group is them... the Church of Christ! Why shouldn’t one just be a Christian?  Why would you want a prefix which tells what type of Christian you are? Why not just belong to Christ. This also allows them to claim that you are not a true Christian and you are not going to heaven, because you don't belong to the one and only, true Body of Christ. Convenient, but ignorant. A denomination is simply a certain type of the same thing, such as a denomination of money. Let's say I had $50 in my pocket. And we'll say that it was a $20 bill, two tens, and two fives. Each of those denominations is a form of paper money. They are different denominations and are of different values but they are each considered to be of the same currency. Boy do you not understand.  Each denomination of money is a part of the whole. It is the different divisions of it. If the whole that you are a part of is not right then you are not right. But according to the Church of Christ denomination, some of the bills are real money but others are not, because a denomination is a "group or thing that has come out from an original group or thing." The number on the bottom of a fraction is called the denominator.  It is the divisor.  The word denomination simply means divisions. Their obvious flaw in this scenario is called "circular logic." Why are they not a denomination? Because we do not want to be part of a division in the body of Christ. Because "they are the true body of Christ!" And why are they the true body of Christ? Because "they are not a denomination!" The word "denomination" comes from the Latin word "nomin", which means "name" and the prefix "de" means "of." So, "de nomin" simply means "of the same name." That is correct and the name should be Christ. Eph 3:14 ¶ For this cause I bow my knees unto the Father of our Lord Jesus Christ,  15 Of whom the whole family in heaven and earth is named, And in the case of the church, it would be of the same name... Jesus!

Paul addresses the issue of denominations in I Corinthians 11:18-19.

He says, "For, in the first place, when you come together as a church, I hear that divisions exist among you; and in part I believe it.

¹⁹For there must also be factions among you, so that those who are approved may become evident among you.   He is not praising them here.  Division is not good.  He rebuked those in error.  (1 Cor. 1:10-13)  Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment.  For it hath been declared unto me of you, my brethren, by them which are of the house of Chloe, that there are contentions among you.  Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ.
Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?
Clearly he is not approving of division.  Some them were Apollos Christians and some were Paul Christian.  This is condemned.   Jesus prayed for unity. (John 17:20-21)  His desire is that we be one.  Division is not condoned!

The Greek word used in this verse for “division” is schism, which simply means a division.

The Greek word used here for “factions” is hairesis, which means dis-unity.

So on the surface it seems as though Paul is condemning these divisions… or is he? In reality, under closer scrutiny, he is actually endorsing these divisions or denominations. Why? Because he says in verse 19 that the divisions allow our congregations to be separated into groups that can be identified as “approved” or “not approved.”  Could it be that you are in that which is not approved?

If I go into a new city and I want to go to a Church of Christ, I simply look in the Yellow Pages under “Churches of Christ.” If I want to go to an Assembly of God, I do the same. This way I don’t unknowingly go to a Church of Jesus Christ of Latter-day Saints (Mormon). I’m sure that the Lord would prefer perfect doctrinal unity in all his congregations, but He knows that won’t happen this side of Heaven. Even the three Church of Christ denominations can’t decide on multiple cups, musical instruments or multiple loaves for communion. So basically were are back to square one, it doesn’t matter so much what you call your church (Church of God, Church of Christ, Church of Jesus Christ, etc.), but more importantly, what you teach. The name is important, you take away from the Glory that belongs to Jesus Christ when you place another name upon it.

Paul also addresses this issue in I Corinthians 12:12-31,

¹²"For even as the body is one and yet has many members, and all the members of the body, though they are many, are one body, so also is Christ.
¹³For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.
¹⁴For the body is not one member, but many.
¹⁵If the foot says, "Because I am not a hand, I am not a part of the body," it is not for this reason any the less a part of the body.
¹⁶And if the ear says, "Because I am not an eye, I am not a part of the body," it is not for this reason any the less a part of the body.
¹⁷If the whole body were an eye, where would the hearing be? If the whole were hearing, where would the sense of smell be? 
   ¹⁸But now God has placed the members, each one of them, in the body, just as He desired.
¹⁹If they were all one member, where would the body be?
²⁰But now there are many members, but one body.
²¹And the eye cannot say to the hand, "I have no need of you"; or again the head to the feet, "I have no need of you."
²²On the contrary, it is much truer that the members of the body which seem to be weaker are necessary;
²³and those members of the body which we deem less honorable, on these we bestow more abundant honor, and our less presentable members become much more presentable,
²⁴whereas our more presentable members have no need of it. But God has so composed the body, giving more abundant honor to that member which lacked,
²⁵so that there may be no division in the body, but that the members may have the same care for one another.
²⁶And if one member suffers, all the members suffer with it; if one member is honored, all the members rejoice with it.
²⁷Now you are Christ's body, and individually members of it. 
 ²⁸And God has appointed in the church, first apostles, second prophets, third teachers, then miracles, then gifts of healings, helps, administrations, various kinds of tongues.
²⁹All are not apostles, are they? All are not prophets, are they? All are not teachers, are they? All are not workers of miracles, are they?
³⁰All do not have gifts of healings, do they? All do not speak with tongues, do they? All do not interpret, do they?
³¹But earnestly desire the greater gifts. And I show you a still more excellent way. 

So we see that God says that there is one BODY of Christ (one Church) but is has many members or parts. He said members not other bodies.  He is writing to a particular congregation and is speaking of individuals.  He is not speaking of different groups or different bodies. Those parts (individual members not parts) all have their own individual callings and functions. Unfortunately, the Church of Christ denomination says to all other members of the body:  "I have no need of you...you are not a part of the body!"   Consider the game of baseball or any game.  Say that the game had been lost for thousands of years.  Then someone finds an old rule book explaining the game of baseball.  Could they not take that book and set up the game just like it was played a thousand years earlier.  In the same way if we take the Bible and follow it and it alone, it stands to reason that we could organize the church just like it was in the first 100 years.  Perhaps it would be good for you to try to take the bible and go back to the Church in the first century.  And be just a Christian nothing more and nothing less.

1Co 3:3 For ye are yet carnal: for whereas there is among you envying, and strife, and divisions, are ye not carnal, and walk as men?  4 For while one saith, I am of Paul; and another, I am of Apollos; are ye not carnal?  5 ¶ Who then is Paul, and who is Apollos, but ministers by whom ye believed, even as the Lord gave to every man?  One cannot take one scripture, and disallow others to make a point.  Divisions are not approved by God.  All scripture must be brought together in harmony.