Byblia ilithyia butterfly
Ilithyia (ill-ITH-ee-uh), or Eileithyia, comes from Εἰλείθυια (Eleuthia), which could be Pre-Greek in origin. The spelling Ilithyia is the Latinized form of Eleuthia and may have first been used by Horace, and Eileithyia is the Greek form, and she is also sometimes refered to as Elysia. She was the Greek goddess of childbirth and midwifery, and her name means "to bring," or "to come," making her The Bringer. On a related note, some research into etymology points to Elysia meaning "to come" as well, and not necessarily the meanings like "blissful" or "joyous" that have been recorded in the past. Elionia may have been another name of hers - she was worshiped at Argos as a goddess of birth. Elithyia has been recorded as a simpler spelling of Eileithyia.
Zeus and Hera were her parents. She is also likely the same as Eileithyia, a Minoan goddess that was slightly older. Eileithyia/Ilithyia was written about by Homer, Hesiod and more, and she had shrines and a cult for a very long time. She had a cave near Amnisos, on Crete, which was said to be her birth place. However, she does have other origin stories. She was often depicted carrying a torch to help bring children out of the darkness. Ilithyia was worshipped at night, outside what is called a pomerium, or religious boundary line. At first she may have been two deities - one for bringing on labor, and who for halting it. There was also some mention of Ilithyia being cognate with the Roman goddess Lucina, or being closely identified with either Artemis or Juno, but researcher Michael Lipka explains that all of them were distinct and appeared at the same time with individual sacrifices or prayers.
In 2015 only 10 girls were given the name Ilithyia, while there are no usages of Eileithyia. However, Ilithia was given to 5 girls in 2011.
It must also be noted that perhaps the most well-known namesake, and the most prevalent search result for this name, is the character Ilithyia from the recent TV show "Spartacus." Also, the Byblia ilithyia, shown in the picture above, is a nymphalid butterfly species also known as the spotted joker.