Jesus, head of all things (Matthew 28:18; Acts 2:36): is also the builder, and head, of His church -
... on this rock I will build My church, and the gates of Hades [or, the unseen world of the dead] will not prevail against it
(Matthw 16:18)
He is the head of the body, the church ...
(Colossians 1:18)
What is the church? It is the people special to Christ, bought with His blood.
... the church of the Lord and God which he purchased with his own blood.
(Acts 20:28)
It is clear that Jesus, having one body, has one church - that one which has been purchased with his blood on the cross.
The New Testament is the written set of teachings for this church. The church following the New Testament pattern is the Lord's church. If we choose to follow something other than the New Testament pattern, we are not acceptable to him.
These people draw near to me with their mouth, and honor me with their lips; but their heart is far from me. And in vain do they worship me, teaching as doctrine [teachings] rules made by men.
(Matthew 15:8-9)
Unfortunately, the scriptures predict that men would depart from this pattern:
I command you therefore before God and the Lord Jesus Christ, who will judge the living and the dead at his appearing and his Kingdom: preach the word; be urgent in season and out of season; reprove, rebuke, and exhort, with all patience and teaching. For the time will come when they will not listen to the sound doctrine, but, having itching ears, will heap up for themselves teachers after their own desires: and will turn away their ears from the truth, and turn away to fables.
(2 Timothy 4:1-4)
The New Testament has much to say to this body of disciples, or christians, that make up His church. We have already seen some things: the need for repentance (changing one's life), the need to confess the name of Jesus Christ, the Son of God, before men, and the need to be baptized for the forgiveness of our sins.
It also teaches about how this church is to be organized, how worship is to be conducted, faith and the christian way of life. In fact it is our complete resource for our faith and our life in Him!
All Scripture is inspired [literally in the Greek, ‘God-breathed’] and profitable for teaching, for reproof, for correction, and for instruction in righteousness, that each person who belongs to God may be complete, thoroughly equipped for every good work.
(2 Timothy 3:16-17)
Christ is the builder and head; the church must wear no other name.
If you are insulted for the name of Christ, you are blessed ...
(1 Peter 1:14)
Therefore names such as ‘Anglican church’, ‘Lutheran church’, or any other name than Christ's, is unacceptable to Him.
Note though that the term ‘church of Christ’ is merely a description and not a formal title. Christ is the title!
(As a note of interest, the word ‘church’ in the original Greek means ‘assembly’: we could correctly describe ourselves as the ‘assemblies of Christ’ - see for instance Romans 16:16.)
We find the New Testament church simple in its organization. The local congregation (or, assembly) is the only body on earth authorized by the Lord: no headquarters, synods, diocese, etc.
So we see -
Now in the church that was at Antioch ...
(Acts 13:1)
to the church of God which is at Corinth ...
(1 Corinthians 1:2)
The government of the church is to be done by a group (more than one) of elders (also called overseers and shepherds), local to each local church:
When they had appointed elders for them in every church, and had prayed with fasting, they commended them to the Lord, on whom they had believed.
(Acts 14:23)
From Miletus he sent to Ephesus, and called to himself the elders of the church. When they had come to him, he said to them, ‘You yourselves know, from the first day that I set foot in Asia, how I was with you all the time, serving the Lord with all humility, with many tears, ... how I did not shrink from declaring to you anything that was profitable, teaching you publicly and from house to house, testifying both to Jews and to Greeks repentance toward God, and faith toward our Lord Jesus. ... Therefore I testify to you today that I am clean from the blood of all men. for I did not shrink from declaring to you the whole counsel of God. Take heed, therefore, to yourselves, and to all the flock, in which the Holy Spirit has made you overseers, to shepherd the church of the Lord and God which he purchased with his own blood.
(Acts 20:17-28)
Note that, in this passage, the same group is referred to as ‘elders’, ‘overseers’[the term ‘bishop’ originally meant this], as well as shepherds. Such are men with special qualifications as given in 1 Timothy chapter 3; Titus chapter 1; and elsewhere. They must be married men, faithful and mature in the faith, and with believing children, amongst other things.
There are no Popes, Archbishops or any other man-made offices in the church of Christ.
Worship also is simple. It needs to be both in spirit (from the heart) and in truth (according to the Lord's commands).
But the hour comes, and now is, when the true worshipers will worship the Father in spirit and truth, for the Father seeks such to be his worshipers. God is spirit, and those who worship him must worship in spirit and truth..
(John 4:23-24)
One of the things about worship in Christ's church is that it is collective. All sing! There is no separation by rank; no distinction between ‘clergy’ and ‘laity’; no division into choir and audience.
Let the word of Christ dwell in you richly; in all wisdom teaching and admonishing one another with psalms, hymns, and spiritual songs, singing with grace in your heart to the Lord.
(Colossians 3:16)
There is room for discretion as to when the church meets for praise, prayer, Bible study, and fellowship; however there are specific directions to meet on the first day of the week (Sunday) to remember the death of the Lord and to give.
When he had given thanks, he broke it, and said, “Take, eat. This is my body, which is broken for you. Do this in memory of me.” In the same way he also took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink, in memory of me”.
(1 Corinthians 11:24-25)
On the first day of the week, when the disciples were gathered together to break bread ...
(Acts 20:7)
Now concerning the collection for the saints, as I commanded the assemblies of Galatia, you do likewise. On the first day of every week, let each one of you save, as he may prosper ...
(1 Corinthians 16:1-2)