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.