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.

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

354. Jehovah had respect for Abel and his gift' means that things constituting charity and all worship deriving from it were acceptable to the Lord. This has been explained already under what 'Abel' means and under 'gift'.