Otis is a company famous for the manufacturing of elevators. The kind that haul you up from ground floor to the 5th floor in your hotel of choice. A surgical instrument referred to as an elevator has a flattish end, sort of like a mini chisel. There are different types of surgical elevators, all with different names. But when a surgeon sends you for an Otis Elevator — the joke is on you if you leave the room to go get it.
No surgical instrument is called an Otis elevator. The surgeon is talking about the elevator in the hallway that just transported the patient to your OR. The one manufactured by the Otis elevator company. ;)