Spitballing here but thought of this as my mind wandered this afternoon. Maybe everyone already got this and I'm retarded, or maybe it rings plausible, i dunno.
C_A as we know can be expressed in alternate symbols. Not talking about the agent-see in particul, but the concept of what the sound of it implies. See Eye A, the all seeing eye atop the A-shaped structure on our dollar bill, the same symbol used by the illuminated secret societies, and captured esoterically as the compass and ruler and capital G. Could it be possible that the words central intelligence agency were a by-product that was apathetically tossed at the letters that were intentionally used for this organization?
Sorta like "Hey these letters of the alphabet match our symbol! C….I….A, that's awesome! We can call it the central intelligence agency and nobody will ever get the REAL meaning!"