When a cicada sheds its nymphal skin, revealing its adult form, we call it ecdysis. You probably call it moulting, and that’s just fine.
Here are a bunch of videos of cicadas moulting:
Here is a Magicicada nymph molting (the 17-year variety) by Roy Troutman:
Here is Tibicen moulting by blackpawphoto (YouTube Link):
Here is a video of a Japanese cicada, the Terpnosia nigricosta, moulting by AntoSan09 (YouTube Link):