Been a while since I watched the relevant eps of ENT. Is the group actually referred to as "Section 31" in those eps?
Not exactly. While talking to his Section 31 friend, Reed makes vague referances to "your section" always with an emphasis on section. And the operative did tell Archer to look up Section 31 of the Starfleet Charter to learn more about him.
They are referred to as Section 31 by name in startrek.com's production reports for Demons and Terra Prime.