If you are a spy for side A, you are called “a spy.”
If you are turned by side B against A, you are then a “double agent.”
So, what are you called if:
Side A finds out you are working for Side B, so they turn you again so you feed false information to Side B under the pretext of spying on Side A? Are you just “a spy” again since you returned to Side A? Are you a triple agent?
Side B sends their double agent from Side A to spy on Side C. What are they called now?