What is the significance of the switch of Sarai's name to "Sarah"?
Gur Aryeh (to 11:29): The name Sarai (now Sarah) refers specifically in her role in partnership with Avraham. Refer to 11:29:1.1:2.
Gur Aryeh: To be more precise, while the Gemara (Berachos 13a) writes, "At first she became a princess to her nation...", our Rashi alters the text slightly - "Sarai - means 'my princess,' i.e. princess to me [alone]." Gur Aryeh writes that it is impossible to be a princess to just one person. Rashi means that she was not yet considered a princess by all.