Genesis 3:20

And Adam called the name of his wife Hava, because she is the mother of all the children of men.

חוה, she is a necessary requirement for the human species to continue life on earth.

כי היא היתה אם כל חי, even though the function of the female of the species listed here also applies to all women after Chavah, she is used as the role model and therefore accorded this name. The reason is that she was the first woman ever to fulfill this role.

ויקרא האדם, when Chavah had originally been placed before him, he had named her just as he had named all the animals, the name חוה, however, was her individual name, not the name of the female of the human species. It is possible to explain that after Adam and his wife had eaten from the tree of knowledge, Adam gave her this name, seeing that due to having eaten from that tree, their libido had been awakened, and they knew that they would reproduce themselves. This is why Adam added: אם כל חי, the meaning of the word חי here referring to the kind of living creatures who possessed the power of speech. Generic names for human beings such as חי here, are also found in Psalms 145,21 ויברך כל בשר, where David does not refer to the animals blessing the name of G’d, but only to the human species doing this. The same applies to Isaiah 66,23 יבא כל בשר, where the prophet predicts that all of humanity in those days will come once a month to Jerusalem or even weekly, to pay their respects to the Lord in Jerusalem. [probably those living near Jerusalem will come once a week, whereas those living farther away will come only once a month. Ed.] The letter ו in the word חוה instead of the letter י was to distinguish her from the beasts of the field.