The stories of Adam and Chava, as well as Kayin and Hevel, pose some interesting questions. Let's take a look. 

"And the man (Adam) said, '...this shall be called "Isha" ("Woman"), for she was created out of man ("Ish"). (Bereshis 2:23). However, after Adam and Chava's sin and punishment, we unexpectedly read, "And Adam called the name of his wife 'Chava', for she was the mother of all life ('Chai')." (ibid. 3:2) Why did Adam apparently change or add to his wife's name? Was she to be called Isha or Chava? Why was the name Chava given after the sin and punishment?

Chazal tell us that Adam and his wife were originally joined as two sides of one body.In fact, before their sin, we do not get the sense that Adam and his wife were very different. Despite Adam's wife having persuaded him to eat the fruit of the Etz Ha-Da'as (Tree of Knowldge), their roles were not established as distinct in any way. Adam's wife was a partner to him - period.

Subsequent to their sin, the roles of Adam and his wife were markedly defined and differentiated. Adam's punishment involved toil in his livelihood, whereas his wife's punishment related to the pain of childbearing, plus some type of submissiveness or meekness in relating to her husband, as elaborated upon by the various commentaries. (See Targum Yonasan ben Uziel, Rashi and Ramban.) The common thread that emerges regarding her punishment is that she would be unable to assert and demand her needs in relation to various circumstances.

It is precisely Adam's wife's punishment that prompted him to declare her as "Chava" - the mother of all life. As the human caregiver par excellence, a woman must, by definition, forgo to a degree her own aspirations and needs for the interests of those to whom she tends. Adam realized that Man's role as a conqueror (Bereshis 1:28) was not especially conducive to mercifully caring for others. One who can forfeit personal needs in deference to those in her care is divinely designated for such a role, and that is the reason that Adam named his wife "Chava" upon her punishment, for the punishment was not merely a curse; it defined her femininity and marked a departure of her identification as a mere uniform, similar partner to him. No longer was she merely "Isha" - a mirror of Man ("Ish"); she was now a unique being with a dramatically different disposition and role.

Chava's curse was presented with this terminology: "...and to your husband will be your desire, but he will rule over you." (ibid. 3:16) Upon his offering being rejected, Kayin was warned that, "...(and if you do not improve, sin lies at the door,) and you will be its desire, but you shall rule over it." (ibid. 4:7) The language in the statements to Chava to Kayin are uncannily similar. How do they relate?

The answer is that Kayin was being instructed to deal with his intense passions by taking a lesson from his parents, regarding whom nearly identical words were used. The curse and redefinition of Chava established a new type of relationship, for until that point, humans were to rule over nature, but they were never given dominion over other humans. Chava's curse gave Adam dominion over her, as a person. Kayin was being told by Hashem that just as Adam was able and expected to rule over Chava so too was he - Kayin - expected to rule over his emotions and exert control. Targum Yonasan ben Uziel explains that Chava was subject to Adam's dominion "whether to merit or to sin" (Bereshis 3:16), and he utilizes the same exact semantics regarding Kayin: "...and you shall rule over it, whether to merit or to sin." (ibid. 4:7) Kayin was to learn that just as Adam now had dominion over Chava and that this dominion was in his hands as to its use, Kayin needed to realize that the human emotional drive is not an equal opposing force (as "Ish" and "Isha") to which one can excusably succumb, but it is a force given to our control (as "Adam" to "Chava"), and it is our job and responsibility to use it for the good.