What can be the name of such a paper-cut case?

The peacock's paper-cut image is similar to the phoenix, and it also symbolizes auspiciousness and happiness. Peacock feathers are gorgeous and elegant. It is regarded as a civilized bird and has the reputation of "Wen Bird". The ancients also summarized the peacock's "nine virtues" according to its living habits, which further promoted the peacock to an elegant realm.

But peony and peacock together are generally called rich flowers or rich flowers. It's hard to name you if you are a peacock. Generally, such paper-cuts include peacock independence, peacock competition, peacock peony and so on.