So, on one mission when you’re trying to talk to Infinity, you end up opening this orb and releasing this forerunner dude who seems pretty badass and crazy powerful. He says some stuff and does some things, never mentioning or hinting at his own name in any way. Then, when that scene is done, Cortana talks about “That Didact”…why the hell would she call him that, and why wouldn’t Chief ask her what she’s talking about?
Not sure if this counts as spoiler, but better to be safe 'cause it’s hard to unread things.
When she accessed the Forerunner database on Requiem, she mentions finding info on an entity called the “Didact” and, based on the context of the information is able to figure out that it is the Forerunner they run into.
I just assumed her being in the system allowed her certain information. Just like how she knew the what the Promethean enemies were called.
The same way she knew what to call the Promethean “Knights”. She accessed requiem’s database, and he was tagged as “Didact”.
Replay the mission leading up to meeting him, when you first come across a Knight she will explain it.