Why would they need to be united under one name or denomination? Whether a person calls themselves a baptist or Evergreen church is irrelevant so long as they are teaching the correct doctrines.
The function of the pastor and elders in a church have this responsiblity guided by the Scriptures.
So you think that Jesus is basically not interested in unity?
Who is the “one” shepherd that Jesus identifies in john 10:16? I don’t see Him pointing out Peter in this chapter as that shepherd.
Not until later.

One generally does not need a vicar until one is absent.
Secondly, there was not a supreme i.e. one leader for the entire church for centuries after the apostles.
Nor is there today, except in the mind of ja4. The leadership of Jesus is a servant leadership, and has nothing to do whatever with “supremacy”. In fact, for the last century we have been blessed to have popes of great humility.
This just happens to be one of your favorite axes to grind, one which I note, is off topic here.
Thirdly, where in Peter’s letters do we see him identifying himself as this “one” shepherd that Jesus mentions?
If you need to discuss the issue of unity around the one Shepherd, then I suggest we open another thread, or use one of the ones open on this topic. There was no disunity among the Apostles, or between them an the Head. If you do not wish to be in unity with the successor of Peter, that is you perogative, but why attack those of us that do? How is our unity a detraction for your faith?
We have differences of understanding that i pointed out earlier. Its part of the human fallen condition. Its true also in the catholic church also. There is a wide range of interpretation of the scriptures in the catholic church. Are you aware that the catholic church has infallibly interpreted less than 20 verses of the Scriptures ?
Another one of your favorite stinkbombs. Off topic, and inaccurate.
How so? Where does Jesus identify this “ONE Flock bit”? What exactly is it?
How is this in ANY way related to the topic? Is there some reason you don’t want to talk about Tradition? Could it be that your questions have been answered, and that you are not able to pursuade anyone here to your narrow viewpoint?
Not so. I’m trying to understand what they mean just as you are. Can you tell specifically what they mean i.e. where your church has interpreted this verse (John 10:16)?
Catholics don’t need to separate verses out and interpret them peicemeal. The Apostolic Teaching makes it quite clear how the verse is to be understood. However, I can’t see that it is related to the topic at all. You sure are doing a lot of spinning and bobbing today.
Not changing it at all but this must be part of this discussion. The catholic church claims to have this “shepherd” i.e. pope in which all of chriistianity to be unitied under.
How is that part of the discussion on the definition of Tradition? There is One Shepherd, who is Christ, and one flock, all who belong to Christ. Jesus ordained Peter to the task of strengthening the brethren (a charge He did not give to any other Apostles), and the Keys. Peter is joined to Christ in the work of shepherding the One Flock. I am sorry, ja4, that you find it so objectionable to realize that there are Catholics in the same flock. It is clear that you don’t want to be connected to us, and that you try as hard as you can to foment division, between yourself and us, and in between Catholics.
We need to since he supposely the first shepherd of the church.
What is this “need” that you have ja4? Since you don’t recognize him as your shepherd, how is that a “need” for you? How is it relevant to the thread topic?
What makes you think they have not? They would all claim that Christ is alone is the supreme Shepherd over the entire church.
If this is true, then they have fallen into the same secular mind about leadership as you have. Jesus Himself said He came not to be served, but to serve. He did not have an attitude of “supremacy”.
Has the catholic offically denounced and excomunicated them?
Why is it so important to you that this happen? Would this be a truimph of the divisiveness you are advocating? Most folks excommunicate themselves, so it does not have to be done by someone else. Truth is not always best served by “denouncing” those that don’t adhere to it. I know it seems to you that it is so important to “denounce” those that don’t believe as you do, but do you think it has really served you well here on CAF?
For example, is Mary the medatrix of all graces? Or is there salvation outside the catholic church? I have seen both position in the catholic church on these issues. Which one is the correct one?
How are either of these related to the topic? It seems to me that you are going thru your usual laundry list of complaints about the Church. If you don’t want to address the topic, ok, but can you take these topics elsewhere?