When I was just a little kid in the early 1950s, the term/code name ["The Truth"] for Jehovah's Witnesses was just beginning to be used interchangeably with the generic term "God's Organization" and "God's People."
After Nathan Knorr took over as President of the Watchtower Society and Fred Franz became Vice-President a few years later there were two basic threads that provided the framework for the modern version of Jehovah's Witnesses. The original version of "The Truth Shall Make You Free" (1943) was followed by the primary study boook "Let God Be True" (1946 - Green) which was just a few years later followed by a revision the original version of "The Truth Shall Make You Free" and a revised version of "Let God Be True" (1952 - Maroon).
It was during the 1950 and 1953 International Conventions in New York that the term "The Truth" first became synonymous with "The Organization" (i.e. The Watchtower). While rank and file JWs were slow to grab on to that nickname for the organization at first, still referring to the Society as "God's Organization" or themselves as simply Jehovah's Witnesses, the substitution of the term "the truth" became locked in as the descriptive name for the Watchtower ("The Truth") in 1968. It was during the International Convention that year that the study book "The Truth that leads to Eternal Life" was released.
The last three paragraphs of that book (pages 189,190) lock in the phrase "the way of the truth" as a substitute for "the way" (a term used by early Christians as a descriptive way to describe themselves and Christianity) as an approved and more or less formal way to describe the Watchtower.
I remember my parents first using the descriptive term "The Truth" in the early 1970s when they would plead with me to "come back to the Truth" or when they refused to consider any objections to the 1975 prophecy ("Johnny, we could never leave the Truth," " We could never take a stand against the Truth.")
I think it is quite interesting that Jehovah's Witnesses have switched from being "Christians" (noun) to members of the "Christian (adjective) Congregation of Jehovah's Witnesses" and have all but abandoned the use of "Bible Students" to describe themselves except when they are in uncomfortable situations when the use of "Jehovah's Witnesses" might prove embarrassing or dangerous.
It must be uncomfortable to call their organization "The Truth" when it is forever changing what it believes and reversing positions on even some of their most basic teachings. Must be why "Let God Be True" is no longer their primary introductory study text.
JV