She was Machan Li's daughter, but was traded to Horse in exchange for various power-ups. She wasn't "Horse's Guy" (that would be Pho), but Horse has been using her as a mastermind to work up plans for bringing him into the Cycle.
Cai Wen still owes Horse some country-tagging plans in exchange for formally freeing her from his service, and the understanding is that she can still think up plans for him.
When she was traded to Horse, her name was part of the deal (as it would have been a connection to her father). Cai Wen proposed the name "Mystique", which she likes well enough.