The 4 Way One Leg Squat is the name for this challenging combination of four different types of one leg squats. The name is because the free leg goes in four different directions, in front, behind, to the side, and to the other side behind.
This includes:
Advanced Shrimp Squat (that is both hands on the back leg)
Dragon Pistol Squat
Pistol Squat
Hawaiian Squat
Credit goes to Al Kavadlo for introducing many of these to me. For a long time I thought the pistol squat was basically it when it came to one legged squatting but then I found out these other moves, which proved harder to master.
For more about bodyweight squats and how to master them, check out The Ultimate Guide to Bodyweight Squats and Pistols. I plan on updating this volume soon with all of these exercises in all the detail I found out in training for them.