באר שבע

The episode of the wells involving יצחק and אבימלך comes to a conclusion in באר שבע. However, it was called באר שבע before they got there. Then, after the covenant between יצחק and אבימלך, it is named באר שבע. Is this the same באר שבע as the one named by אברהם? If so, why did they name it the same name all over again?

רשב"ם writes that this was in fact a different באר שבע from the one in the times of אברהם. However, an interesting explanation is given by the ספורנו. He writes that the name in אברהם's time was בְּאֵר שָׁבַע. After the episode with יצחק and אבימלך, it was renamed to בְּאֵר שֶׁבַע. It is very interesting that this theory can not be disproved. Any time that the city is mentioned until now, it appears either at the end of a פסוק, or an אתנחתא. Even if it were בְּאֵר שֶׁבַע from before, the סגול would have always changed to a קמץ. So we have no way of knowing if it called בְּאֵר שָׁבַע because of its position in the פסוק or if it is because that is really its name. ספורנו writes that it was in fact its name since it was only named as such to reflect the vow that אברהם made. Now that it reflected the number seven as well, corresponding to the seven wells that were found, it was changed to בְּאֵר שֶׁבַע. 

One year, on ראש השנה, the בעל קריאה said בְּאֵר שֶׁבַע and I almost corrected him based on the ספורנו. But I didn't.