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.

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

287. Verse 20 And the man called the name of his wife Eve, because she was to be the mother of all living.

'Man' (homo) here is used to mean the member (vir) of the Most Ancient Church, that is, celestial man, and 'wife' and 'mother of all living' the Church. It is called 'mother' because it was the first Church of all, and 'living' because of its faith in the Lord, who is Life itself.