The name 'Eve' comes from the Hebrew word חַוָּה or 'Chava,' a form of the word for life, which is why she is called 'the mother of all living.' She represents the church, and is called 'mother' because this was the first Church of all, and 'living' because of its faith in the Lord, who is life itself.

(références: Arcana Coelestia 287-291, Genesis 3:20)

342. That the second born of the Church is charity becomes clear from the things which the Church conceives and gives birth to, which are nothing other than faith and charity. The first of those born to Leah by Jacob had a similar meaning. Reuben meant faith; Simeon, faith expressed in action; Levi, charity, Genesis 29:32-34. This also was why the tribe of Levi assumed the function of the priesthood and became representative of the shepherd of the flock. Being the second born of the Church, charity is referred to as 'a brother. and is called 'Abel'.