Since ‘et YHWH’ is the direct object of ‘quanah’, could not the verse be indicating that Havah has expended effort (pregnancy and child birth) in order to give YHWH a man [another 'ish' to replace Adam who is now doomed to die] so that life would not end and through this cycle death eventually would be defeated by the promised seed?!?

Adam recognizing this amazing purpose of renewing of life, named her Havah in honor of her role as the life extender (without which human life would have ceased). Her ‘ezer’ role is not the same as his role, but complimentary to it even as the Ruach compliments the Father and Son.

Tolstoy wrote a great short story based on this biblical theme.

It is ironically entitled “Family Happiness.”