Why was the well called "Be'er la'Chai Ro'i"?
Rashi (citing Targum Onkelus): It means, "the well upon which a living angel appeared." 1
Targum Yonasan: It means, "The well upon which the One who lives and exists appeared."
Gur Aryeh: Where is the angel mentioned in the Pasuk? The word "la'Chai" refers to the angel, who remains alive.
QUESTIONS ON RASHI
Rashi writes: "According to the Targum, this translates as, 'the well upon which the living angel appeared.'" This differs slightly from the verse, which states "appeared to me"(Ro'i).
Gur Aryeh: The verse does not say :Therefore she [Hagar] called the well..." (Ka're'ah), but rather "called" (Kara). From that day onwards, not just Hagar, but everyone would refer to the well by this name.