What is the connection between the beginning of the Pasuk and the end (plus the following episode?
Seforno: Now that (for the first time) Yitzchak built a Mizbe'ach and called out in the name of HaSh-m, he merited 1 that his shepherds dug a well without opposition, that Avimelech came out to visit him and enter into a covenant with him, and that from now on, the Pelishtim left him in peace.
Why did Yitzchak not give the new well a name?
Ramban (to 26:32) and Rashbam: He did, but only after Avimelech arrived and entered into a covenant with him. It was only then that his shepherds came and told him about it. 1
The delay itself seems to have been an act of Hashgachah Pratis, as it was min ha'Shamayim that the well should be called 'Shiv'ah,' and the town 'Be'er-Sheva.'
Why does it say here "va'Yichru"? Below (26:32), it says "Asher Chafaru"!
Malbim, Ha'amek Davar: Yichru is the initial digging. Chafaru refers to finishing the digging. Ha'amek Davar - the Torah teaches that (a) first he built a Mizbe'ach, a place for Korban and Tefilah, and called in HaSh-m's name; (b) then he built his tent for dwelling, and (c) only after, he began digging a well, for more comfortable dwelling.