The maftir of Noach says וַיִּקַּ֨ח אַבְרָ֧ם וְנָח֛וֹר לָהֶ֖ם נָשִׁ֑ים שֵׁ֤ם אֵֽשֶׁת־אַבְרָם֙ שָׂרָ֔י וְשֵׁ֤ם אֵֽשֶׁת־נָחוֹר֙ מִלְכָּ֔ה בַּת־הָרָ֥ן אֲבִֽי־מִלְכָּ֖ה וַֽאֲבִ֥י יִסְכָּֽה. Rashi says יסכה – [זו שרה, על שם]א שסוכה ברוח הקודש, ושהכל סוכין ביופיה, ולשוןב נסיכות, כמו: שרה לשון סררות. Sarah is identified in the possuk with two names, יסכה and שרי in the same possuk. Why is she called by two names in the same possuk? And why is the name יסכה alluding to her ruach hakodesh spelled out here and never again and why not mention it in the context of Hashem acknowledging the greatness of her prophesy?
The second to last possuk in Noach says וַיִּקַּ֨ח תֶּ֜רַח אֶת־אַבְרָ֣ם בְּנ֗וֹ וְאֶת־ל֤וֹט בֶּן־הָרָן֙ בֶּן־בְּנ֔וֹ וְאֵת֙ שָׂרַ֣י כַּלָּת֔וֹ אֵ֖שֶׁת אַבְרָ֣ם בְּנ֑וֹ וַיֵּצְא֨וּ אִתָּ֜ם מֵא֣וּר כַּשְׂדִּ֗ים לָלֶ֙כֶת֙ אַ֣רְצָה כְּנַ֔עַן וַיָּבֹ֥אוּ עַד־חָרָ֖ן וַיֵּ֥שְׁבוּ שָֽׁם. The parsha of Lech Lecha opens וַיֹּ֤אמֶר י״י֙ אֶל־אַבְרָ֔ם לֶךְ־לְךָ֛ מֵאַרְצְךָ֥ וּמִמּֽוֹלַדְתְּךָ֖ וּמִבֵּ֣ית אָבִ֑יךָ אֶל־הָאָ֖רֶץ אֲשֶׁ֥ר אַרְאֶֽךָּ. What is the nature of these two travels?
The Ramban asks why are we not introduced to Avraham as a tzaddik but instead are merely introduced to him as a man told to leave his home? The Maharal (Netzach Chapter 11) explains that we are being taught that Avraham is not chosen merely because he is a tzaddik and hence if future generations are not so righteous they will no longer be chosen, rather we are chosen by Hashem because he desires to choose Avraham and his children no matter what state they are in.
Parshas Lech Lecha is when Avraham is chosen to be a sperate nation apart from everyone else. The last possuk in Noach says Terach died. Rashi notes that Terach didn't actually die at that point but Terach is dead to Avraham when he starts his journey to Lech Lecha. In other words, at this point Avraham is no longer connected to Terach, he is starting his own legacy (see Gur Aryeh.) Originally, Terach also was going to travel to Eretz Yisrael, he also was on the path to being able to transform his life and be the patriarch for the Abraham clan . However, he never is quite able to complete his journey, he gets stuck in Charan. The Terach life is the life of the idol worshipers, who, as the Rambam explains, started with noble intensions to serve the messengers of G-d but they got lost along the path and never ended up completing the journey of reaching to Hashem. They got stuck on the road with the emissaries. Avraham sees beyond the forces in the world, he sees the True Master, Hashem and seeks Him out. He is able to get to the end of the path that was embarked on the by idol worshipers.
Rashi (end of Noch) says that Avraham was thrown into a fire by Nimrod for rejecting idols and after he survived and Haran was given the choice between Hashem and the idols he also chose Hashem and he was thrown into the fire and perished. Rav Moshe Shapira explains it wasn't merely that Haran was hedging his bets and that he would choose what seemed better after seeing the results for Avraham. The act of Haran was a reflection of his nature. His was not a trailblazer, a man able to forge his own way, like Avraham. This is why Avraham is the first of the Avos. Haran wanted to know the truth an then he would stick to it faithfully, no matter the circumstances. Haran is the father of the אמהות. He is the father of Sarah, the grandfather of Rachel and Leah, and the father-in-law of Lot, who leads to Rus and the Messianic line. The trait of Haran is the trait of the imahot, to see the truth and stick to it no matter how hard it is.
The ability of Sarah to be Yisca, to be a great prophetess, stems form the misaras nefesh of Haran. His acknowledgement of the truth to the ability that he gave his life for it yielded the ability for his offspring to cling to Hashem even in the darkest places. It is due to her being the daughter of Haran, that Sarah is Yisca, that she has such spiritual clarity of vision. Hence, when she is mentioned as a daughter of Haran her name is Yisca, for it is the relationship with Haran that makes her Yisca. It is her role as the daughter of Haran that makes her Yisca. But in her role as the wife of Avraham, the starter of a new nation, no longer connected to the past, her relationship to her father is not mentioned, her essence is being Sarah, the wife of Avraham, the matriarch of Klal Yisrael (see Gur Aryeh end of Noach, based upon article by R' Yehoshua Shapira, יסכה זו שרה – פרשת נח.)
The Sarah and Avraham of Parshas Noach were part of the greater Terach family. They where members of a family which started seeking the truth but didn't follow through. In Lech Lech, Avraham and Sarah are a new dynasty, no longer connected to the past. All relationships to past self identities, children and grandchildren of Terach, Yisca etc. are removed and they embark upon a journey of Lech Lecha, of self exploration to find their own way, their own destiny.