[10] It is possible that sometimes the name Haya was written logographically as NAĜAR, though this sign could also be read as a variety of other theonyms, for example Alla and Ninildu.
[4][1] Miguel Civil suggested in 1983 that it was a cognate of the theonym Ea, though he noted these two gods were considered separate in Old Babylonian sources.
[13] As of 2016, the proposal that a connection existed between Haya and Ea (and by extension with Eblaite Hayya) was still considered plausible,[10] though it is not universally accepted.
[10] An Old Babylonian text from Nippur indicates that the peacock was referred to as dḫa-iàmušen, but no connection between this bird and any aspects of the god's character has been established so far.
[28] An alternate name of the Hattian grain goddess Kait, written ḫa-i-a-am-ma, might have been derived from Haya, though it might also have a presently unknown Hattic etymology.
[29] The earliest known reference to Haya has been identified on a school tablet from Shuruppak the Early Dynastic period, though the context in which his name occurs on it remains uncertain.
[32] A hymn from the reign of Rim-Sîn I of Larsa also associates him with his city, and states that he was believed to dwell in the Ekišnugal, the temple of the moon god Nanna.
[19] Excavations indicate that in the Old Babylonian period, a temple dedicated to Haya existed in Shaduppum, a small city located near modern Baghdad.
[10] The exorcism formula Gattung II invokes Haya alongside Nisaba, and describes him as the "solidifier of the boundaries of vast heaven.
[10] It describes Haya's roles as a father-in-law of Enlil and as a divine accountant, mentions a connection between him and Ur, and implores him to bless the king.
[36] It also states that he is responsible for marking down the years of a king's reign of the "tablet of life," a mythical artifact used by gods to keep track of deeds of mortals, though in other compositions this item is instead associated with deities such as Nisaba, Ninimma, Nungal or Lammašaga.