Why did they call the new well that Yitzchak's shepherds dug, 'Shiv'ah'?
Moshav Zekenim, Seforno, Malbim: It is because it was the seventh well that they dug. 2
Why does it say that they called the town Be'er-Sheva? Avraham already called it 'Be'er-Shava'!
Seforno: Because Avraham called it by that name on account of the Shevu'ah, whereas Yitzchak also had in mind the seven wells (refer to 26:33:1:2 and the note there), at which 'Sheva' (with a Segol) also hints. 1
Rashbam: This is not the same town as that of Avraham, as there are two towns that share that name. We find "Be'er Sheva Asher li'Yehudah" (Melachim I 19:3).
Ramban (to 26:32): Yitzchak's servants re-opened the same well that Avraham dug and which the Pelishtim stopped up together with the other wells that he dug. 2 He called the well Shiv'ah, and the city Be'er Sheva, like his father called them.
Moshav Zekenim: Its name ceased after Pelishtim plugged up the well, and Yitzchak returned the name when he opened it. If the name was due to the Shevu'ah, they should have called it Shevu'ah! Rather, it was due to the well. 3
Malbim: Avraham called only the place Be'er Sheva. Yitzchak called also the city Be'er Sheva.
Ha'amek Davar: After Avimelech and his nobles annulled the Bris, they changed its name, lest it mention their guilt. Now that they made a Bris with a curse (it is unlikely that anyone will annul it), and they dug the seventh well, the name returned and remained. It says here, "Al Ken Shem ha'Ir," to teach that it did not change again; whereas above it says, "Al Ken Kara" (21:31).
The change of vowel is not a proof. 'Be'er Sheva' appears 33 places in Tanach. When the Neginah of 'Sheva' is an Esnachta or Sof Pasuk, this changes the Segol into a Kamatz ('Shava'). All other times, it is 'Sheva' with a Segol! (EC, PF)
Ramban: Yitzchak called the town Be'er-Sheva due to the well. (He cites "Ki Sham Nishbe'u Sheneihem" - 21:33), which implies that Avraham named the city due to the Shevu'ah. - PF)
"Ki Sham Nishbe'u Sheneihem" (21:33) implies that Avraham named it Be'er Sheva due to the Shevu'ah! Perhaps it was also due to the seven sheep (21:28-30). In any case, the name Be'er Sheva was not appropriate after the well was stopped up. (PF)
What are the connotations of "Ad ha'Yom ha'Zeh"?
Rashi (to Bereishis 22:14): Up until the time of whoever reads this Pasuk.
Here it connotes that Be'er Sheva is not in Eretz Pelishtim. Above, it says that Avraham lived in Eretz Pelishtim, and he was in Be'er Sheva!
Moshav Zekenim #1: It was in Eretz Pelishtim. Yitzchak was expelled only from Gerar, which is the primary Eretz Pelishtim. Afterwards, it says that he went to Nachal Gerar.
Moshav Zekenim #2: Actually, it is not in Eretz Pelishtim, just close to it. Be'er Sheva was in the southern extreme of Eretz Yisrael - "mi'Dan v'Ad Be'er Sheva" (Melachim I 5:5). The animals of Avraham and Yitzchak were in Eretz Pelishtim.