Huh? Where did you get the idea there was an agency called Section 31 before? I mean, it wasn't a name at all to begin with; it was the line in the Starfleet Charter (Article 14, Section 31) that was ambiguously enough phrased to give Control a plausible-sounding excuse for the cabal's existence.
The ENT episodes featuring Harris never actually refer to his group as Section 31, although Reed does call it "your section" on a couple of occasions; Harris only cites Article 14, Section 31 as his justification for his group's activities. The Good That Men Do picks up on this and treats "Section 31" as Trip Tucker's nickname for the unnamed group; previous member Tinh Hoc Phuong calls it simply "the bureau." In my subsequent ENT books, I've treated it largely as a nickname myself.