statue animation, ritual animation, or consecration of images/idols.
The sacred image and statue as living ensouled being (ensoulment rites)
Egyptian Tradition Known as the Opening of the Mouth ceremony, which is a ritual of animation and consecration allowing the god's ba (manifest spirit or power) to inhabit the statue.
Mesopotamian Tradition Referred to as the Mīs Pî (mouth-washing) and Pit Pî (mouth-opening) rituals, similar to the Egyptian version, focusing on animating divine statues
Greek and Roman Tradition (Including Theurgy and Hermeticism) Generally called statue animation or the telestic art (from Greek telestikē, meaning initiation or perfection through ritual), often within the broader practice of theurgy (ritual magic to invoke divine powers). "Ensoulment" appears in later philosophical texts (e.g., Neoplatonists like Iamblichus) to describe drawing daimones (spirits) or divine essences into statues.
In Hindu and Tantric practices (influenced by Vedic roots), it's called Prana Pratishtha (or Pran Pratistha), meaning "establishment of life breath" or infusing prana (vital energy/spirit) into the idol. This is a consecration rite transforming a lifeless statue (murti) into a living deity.