Mayura is the peacock, and the image behind the name is a bird standing with its long tail carried out behind it, level with the ground. The posture puts the legs in that position: the body is horizontal, balanced across the elbows, and the feet trail behind like the train. It is one of the more transparent of the classical resemblances.
The peacock is also the mount of Kartikeya, the war god, and it appears widely in Indian art and in the iconography of several deities. The manuals make nothing of that, and the atlas does not attach it to the posture as an intended meaning. The naming here works by shape, as it does for the cockerel, the locust and the crocodile.
What makes mayurasana notable within the corpus is that, with kukkutasana, it is one of only two postures in the earlier manual that ask the arms to carry the whole body. The Hatha Yoga Pradipika is otherwise a book of seats. The presence of two arm balances in a list of fifteen is a reminder that the early repertoire was not exclusively meditative even at its narrowest, though the balance of it is overwhelmingly so. Mallinson and Singleton's Roots of Yoga collects the primary descriptions in translation and lets the proportions of the early corpus be read directly rather than inferred from later practice.