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.

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

361. Verse 7 If you do well, is there not an uplifting? And if you do not do well, sin is lying at the door. And to you is his desire, and you have dominion over him.

'If you do well there is an uplifting' means, if your desires are good, charity resides with you. 'If you don't do well, sin is lying at the door' means, if your desires are not good, charity does not exist, but evil.' To you is his desire, and you have dominion over him' means that charity wishes to reside with you, but cannot because of your wish to have dominion over it.