After Draper kills the Hybrid on Io, she calls for assistance. " "Rocinante" This is Draper." When Holden and his crew picked up Draper in the Razorback with Avasarala, they had already changed the transponder and name of their ship to, "Pinus Contorta." Unless Draper had overheard the crew calling the ship by their Holden-chosen name, she wouldn't have known about this update.
When Draper and the hybrid fall from great heights on Io, they both hit with a big thud. However, given Io's much lower gravity, a 200-pound person on Earth would only weigh 36 pounds on Io, thus they would have fallen more slowly and would have soft landed.