I'll go with "headset cup remover tool"
Just kidding.
I use a hardwood dowel and a dead blow mallet. The dowel is placed down inside the headtube with the edge catching the headset cup and then I strike the dowel with the mallet firmly. The hardwood does not deform when struck and won't deform the cup, and the dead blow mallet keeps the whole shebang from wiggling in my hands like a rubber mallet would. Work in 30 degree increments around the cup and walk it on out.
Make sure you are catching the headset cup edge with the dowel and not any internal headtube reinforcements which may be on your frame.
Do NOT use a metal punch or wedge in place of the dowel, you could waste the cup and in extreme cases the frame.