Ned, my feeling is that the name changes are just an outer sign of what was going on at a much deeper level, all along. The people running the show were always pulling smoke-and-mirrors stunts to disguise their true motives -- and not just towards the outer world, but towards all of us ignorant second-class saints as well.
I was involved with the church in Ames during the time that you designate as "the Blitz." But do you know what? Not once did I hear anyone use that term,
ever. I first learned about it decades later, here on the internet. Back then, we had large-group meetings, and home-group meetings, and Task Force teams, and musical groups... which all went under the umbrella term "ISU Bible Studies," because that allowed us to use campus facilities. But among ourselves, we referred to our group simply as "the body" or "the saints in "Ames" (as distinguished from "the saints in Lawrence" or wherever). We had no real name at all, although we used countless names for our various activities.
Further, there were secret groups, such as THEOS, which we were told we should never mention to outsiders, since it was Jim's cover for his publishing enterprises.... But now that I look back on it, I can see that by admonishing us to keep things hush-hush, the leaders were also effectively preventing us from asking any questions.

Jim and his small cohort of fellow schemers liked to keep things fluid within the church. We were constantly being organized into new teams with confusing new assignments. They kept us too busy to ask questions about who was making these decisions, and why. Each grand new plan was simply presented to us as a
fait accompli, and we did our best to keep up. Sadly, I didn't do such a good job of keeping up. I grew quite ill from the strain; and when the M.D. recommended certain medications, my team leaders promptly sent me to a private meeting with an elder, whose counsel mainly boiled down to: "Nobody but us knows what's best for you."
But who were they -- these people who claimed to know the will of God? They never said. They never identified themselves, to us or to anyone else. They never told us that Jim had founded the church. (He was out of town a lot.) They never told us that he claimed to be an apostle. They never told us about his background in the Plymouth Brethren.... They just told us what we were supposed to do.
What it boils down to is this:
These proclaimers of faith did not have enough faith to trust their own church members with the truth about what they were doing. So how could they possibly be truthful with outsiders?