Many churches have special names, but the New Testament church has no name. Denominations have proper names. The word “denominate” means to “name” something. The New Testament church is called the house of the Lord, the family of God, the body of Christ, and the kingdom of Christ (Galatians 6:10; Ephesians 1:22-23; Colossians 1:13; Hebrews 3:5-6; 1 Timothy 3:15), with no proper name.
The individual members of the New Testament church have a proper name. Their name is not “disciple,” though they are disciples (Acts 9:1). Their name is not “brethren,” though they are brothers and sisters (Acts 9:30). Their name is not “saints,” though they are saints (Acts 9:32). Their proper and divinely given name is “Christian” (Acts 11:26; 1 Peter 4:16), but to call the church the “Christian Church” is to denominationalize that great institution.
To speak of the New Testament church as “the church of Christ” is right as it is to speak of it as “the church of God” (Romans 16:16; 1 Corinthians 1:2), but neither is a proper name. To speak of “Church of Christ” congregations, “Church of Christ” preachers, is to denominationalize that church. The New Testament church has no proper name.
Learning from God's Word 
The pagans, 500 years before Christ,used the word church to identify their buildings used for religious work and worship. That is the first definition given to it in Oxford English Dictionary, 20 Vol. set. I am disposed to refer to us as the called out of God and/or Christ. Never use it in the sense of a name or denomonationalise ourselves. I try to avoid using names an d titles not set forth in Holy Scripture as God approved. I like your approach.
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Denominate could also be a sort of division, for example a one piso or a one dollar or any currency changed into cents.
The fact is church is in singular form and possessive form {Matthew 16:18}. Another fact is that, there is only two sense about the church the local church and the universal church like for example the seven churches in Revelation chapter two and apostle Paul’ epistle to the churches like church of Rome, Corinth, Galatians, Achaia to their own houses and etc. When apostle Paul gave a greeting to the universal church Roman 16:16.
Denomination or divisions is not good in the sight of God to quote “Now I beseech you brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that that there be No divisions among you, but that ye be perfectly joined together in the same judgement. 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 am Apollos and I am of Cephas, and I of Christ. Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul? {1 Corinthians 1:10-13}.
When Paul wrote a certain local churches and mentioning church of God he is referring Christian people or the saved ones by the blood of our Lord Christ Jesus. Therefore to name a congregation to a certain congregation as the church of God in not proper name but to a certain place followed of church of Christ is the proper name, in Christ or the church of Christ.
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It is interesting that so much is written, discussed, and defended concerning the singular expression “church of Christ” when inspiration itself never mentions it. All arguments for the singular expression are based upon the plural in Rom.16:16. Yet the New Testament is void of such defenses. The “nameless church” is named by men with an expression that is never given by inspired personnel as though it is THE name of the church! I like Charles’ use which gets away from denominating a name. Rom.16:16 would be “the assemblies of Christ,” or “the called out of Christ,” or “the congregations of Christ.”
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