Here posted is how a group calling themselves Church of Christ (not the INC) 'proves' their claim regarding the name of the Church: http://www.tftw2.org/BCC/courses/bcc_cob_l5.html
Christ promised to build His church (Matthew 16:18). He purchased it with His own blood (Acts 20:28). He is the Savior of it (Ephesians 5:23). He is the head of it (Colossians 1:18). It is only natural that the church should wear His name to honor its founder, builder, Savior, and head. So when Paul wrote to the church at Rome, and sent along the greetings of the congregations in his area, he said, "The churches of Christ greet you" (Romans 16:16). Then in speaking to the church at Corinth, he said, "Now you are the body of Christ, and members individually" (1 Corinthians 12:27). Since the body is the church (Ephesians 1:22-23), then he was simply talking about the church of Christ. It is also called the church of God (1 Corinthians 1:2; Acts 20:28), the kingdom of God (1 Corinthians 6:9), the kingdom of Christ (Ephesians 5:5), the kingdom of His dear Son (Colossians 1:13), the kingdom of our Lord (2 Peter 1:11), the church (Acts 13:1), the church of the living God (1 Timothy 3:15), the church of the Firstborn (Hebrews 12:23), etc. So the church is not called by only one name. Remember, that which belongs to God belongs to Christ and that which belongs to Christ belongs to God. Also, those names all refer to the church that Christ built. If it is not the church of Christ, then whose church would it be? It would seem that one would not really want to get away from the Scriptures to choose another name for the Lord's church. Let us stay with the Bible. Let us call the church what the Bible calls it. Then we will be right.
The following are from the Pasugo I skimmed through some time back. Take note how similar, which would make you think they're from the same author/group:
PASUGO, October 1998, p.3
The will of the Father is for all men to be gathered under one head who is Christ. To be gathered in Christ, one must become part of His body which is the Church (cf. Rom. 12:4-5; Col. 1:18). The Lord Jesus Christ referred to this Church as "my church" (cf. Mt. 16:18, NIV) and was called by the apostles as Church of Christ (cf. Rom. 16:16). Thus, joining the Church of Christ is God's will that must be obeyed to attain salvation.
PASUGO, October 1998, p.4
But what the lord Jesus Christ will save is His body which is the Church:"For the husband is the head of the wife, as also, Christ is the head of the church; he is the Savior of the body."(Eph.5:23,NKJV)"And he is the head of the body, the church."(Col.1:18,Ibid.)There are not many bodies or churches of Christ but one. So thos to be saved are ...members of one body"(Col.3:15, NIV). For truly, Christ founded only one Church (Mt.16:18) for which He gave up his life that those who joined it by faith be redeemed from their sins:"Take heed therefore to yourselves and to all the flock which the Holy Spirit has appointed you as overseers, to feed the church of Christ which he has purchased with his own blood." (Acts 20:28, Lamsa Translation)
PASUGO, January 1999, p.17
Ang tinutukoy na "isang katawan" ay ang Iglesia na pinangunguluhan ni Cristo (Col. 1-18). Ang pangalan ng Iglesiang ito na itinatag ni Cristo ay Iglesia ni Cristo (Mat. 16:18; Roma 16:16).
Translated:The "One body" referred to is the Church headed by Christ(Col. 1-18). The name of this Church that Christ established by Christ is Church of Christ (Mat. 16:18; Rom. 16:16).
PASUGO, September-October 1992, p.3
There was only one church built by Crist and this is called by other names, one of which was Church of God. This is because what is of God is also of Christ (John 16:15,17:9-10)
This bolsters what we all hear time and again that the INC is not unique in its teachings, with doctrines that are adaptations of its predecessors of which its founder Felix Manalo was a member of one time or another. INC preaches a mish-mash of beliefs and picks out any doctrine and their defense thereof from different religions whatever may be convenient.