The answer to your question.........it can be deduced by the application of Occam's razor.
Once martindale pontificated that "word over the world" was complete.......he was exterminating the language and administration (wierwille's) of the past and ushering in the new "man of god and from on high." No longer would there be WOW Ambassadors.....and the Rock of Ages was closing shop, too. By the mid-1990s.......old wierwille tapes or music tapes were deemed "old wineskins" and could get you possessed!!! Martindale mandated that the Way Household be SANCTIFIED.
Way Disciples were enlightened with the present truth.
Way Corps were taught The Way of Abundance and Power......heightened spirituality from the older version.
Martindale, the doofus from Okieland, simply attached "Way" to "Disciples"...........duh. He wanted to distance himself from wierwille's terms and old wineskins. Surely, it wouldn't be right to call them "Disciples of Christ"........that description was already taken. And besides, you can't build a cult following by adhering to what other church denominations are doing.
But, my friend........Occam's razor clarifies to us that the simplest solution is the right solution to the question. Everything in wierwille's path was to be built on the foundation of the WAY.........not the Bible, not the Scriptures. The Way. A term that held a double-meaning. A deceptive and obscure meaning to a narcissist. Wierwille skewered Kenyon's material on "The Way" and built his organization (pyramid) with just enough scripture verses to conceal his intended agenda, a jaded way. And, the WAY corps.......indoctrinating the youth into an army of zealots and strict loyalists to twi-servitude, not God.
Heck, throw in Way Builders......whydon'tcha. LOL.
Or, Way Productions.
Now, maybe......all this stuff was just a marketing scheme to differentiate his organization for the surrounding churches. Could be. But looking back at all this......I see a serial plagiarist, predator and false teacher with ulterior motives. The whole damn thing went belly-up shortly after the false teacher left the scene, feet first.
And again, Occam's razor......the Scriptures indeed describe the seductive attributes of a seducer and false prophet. Wierwille fits that description.