With all deference to the pastors and the people who are really invested in growing COGOP, I ask what difference does it make? Locally, in some places, maybe it makes a real one, I dunno.
Doesn't the "dba" names (Crossroads Chapel, Reunion, etc.) usage take away most of the head-scratching that goes with the "of Prophecy" tag? Or, is it not enough?? I can see where someone coming to, say, Crossroads Chapel, loves it, enjoys everything and everyone there, wants to make roots and says, "A'ight, let's get down to it. What exactly would I be joining if I join you? You talk about these events, conferences, assemblies and all that are not around home, here. Who are all these other people and why does that matter to me?" Then, they get a little more info about the "of Prophecy", its history, the looong explanation about all of that and where it is today...... is that offputting? Sure seems like it would be, but then, I don't know if that's how it plays out in a more or less typical case or not. Do you just avoid altogether?
Do you gloss over it (not to be deceptive, just to not give unnecessary history lessons on things that really don't matter for the future)?
Then, if it is that big of a deal locally, how do you ever begin in the current environment to change it? The COGOP IA is still primarily American, southeastern at that. The "change" theme has always been a harder sell in COGOP. The word "change" now is about as bitter as ever with the current political situation, and don't think people don't take the filters from the civil/political arena and use that in the church. They certainly do. Seems to me like, on balance, a problem that calls for a lot of creativity and flexibility locally, but not, as PG has described other disputes, a hill you want to die on.
I think it's what you call a conundrum.

Human government bears the same relation to hell as the church bears to heaven. (David Lipscomb, On Civil Government, 72).