Parshat Toldot: Beer Sheva or Shava?

This may seem trivial. And to be honest, I may be completely wrong. But I can’t help thinking there’s something deeper behind the names Avraham and Yitzchak seem to give to the city where they each forge a treaty with Avimelech.
Before we proceed with the evidence, we begin with a disclaimer: I am aware that there are words whose vowels change when they land on the cantillation marks of “Etnachta” and “Sof Pasuk.” The change usually involves a segol (the “eh” sound) or a patach (the “ah” sound) becoming a kamatz (more like an “uh” sound). Names, such as “Yefet/Yafet” and “Peleg/Paleg” are prime examples of the former, while Canaan and Mitzrayim (Egypt) are classics in the latter category.
In Chapter 21:28-31, Avraham gave 7 sheep to Avimelekh in exchange for peace (don’t we wish it were that easy today?), then he called the name of the place “Beer ShAva, because they both swore (nish’b’oo) to one another.” Note, of course, that the word “Shava” has an “Etnachta” mark under it. But was the city named for the seven sheep, or for the swear? If the former, it should be Beer Sheva (7). But if it’s for the swear, it should be Beer Shava (on account of the swear).
It seems the jury is out on this one. Targum Yonatan thinks the city was named for the seven sheep. The Malbim and Alshikh say it was named for the swear (Alshikh even raises this discussion!). And Radak thinks both events were included in the city’s name calculation.
In Yitzchak’s case, Avimelekh similarly makes an agreement with Yitzchak, which they swear to maintain (26:31). After Yitzchak sends Avimelekh and Fichol on their merry way, Yitzchak’s servants inform him that they’ve found a well – from all indications, it is the seventh well in Yitzchak’s arsenal.
They call the well “Shivah...” (26:33) Rashi claims the well is thus named because of the swear. Seforno claims the well is thus named because it is the seventh well. Chizkun argues that the well was named for the city they were in – the one that had been named by Avraham.