(Genesis 3:20) "And the man called his wife's name Chavah (Eve)." She was given to him for his life (chiyut), and she counsels him like a serpent (chivya).
Why Adam Named His Wife Chavah, Giver of Life
Yalkut Shimoni on Torah 33:2
(בראשית ג כ) וַיִּקְרָא הָאָדָם שֵׁם אִשְׁתּוֹ חַוָּה. נִתְּנָה לוֹ לְחִיּוּתוֹ, וּמְיַעַצְתּוֹ כְּחִוְיָא.