It's possible that she learned about Rasputin through the Hive directly, who were present in the Cosmodrome when the Fallen found the first of Rasputin's terminals, and who were present when you activated the Last Array. The Hive especially, being as information-centric and -capable as they are, surely moved to intercept whatever signals were sent over the array after its activation, thus learning of the Warmind, which eventually culminates (for now) with your defense of Rasputin from Omnigul and her minions as they try to "capture" him.
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I guess but that whole concept still confuses me. Also, if half her fireteam died before she got to the door of the temple of crota, and then the rest died before they could kill his soul, where did she learn about the hell mouth being the portal to his "realm"? Did she learn that while she was hiding?