Makor is Hebrew for source, or fountain, or spring.   Here are some of the sources for the inspiration of the name and how it applies:

• In Pirkei de-Rabbi Eliezer 30, the well of Hagar is none other than the healing well the Divine made at the dawn of Creation.  This well later accompanies the Israelites through the desert and becomes known as Miriam's well.  Perhaps this well too comes from the tears of those who grieve.    (pg. 35 The Jewish Book of Days)

• In the Torah, just after Miriam dies, the people complain they have no water to drink.  Rabbinic interpreters conclude the well dried up when Miriam died (Song of Songs Rabbah 4:14). Only after Moses goes into the wilderness to search for it does the well reappear.  But the well is not gone.  The Babylonian Talmud (Shabbat 35a) tells us the well can be found to this day in the waters of the Sea of Galilee.  The Shulchan Arukh (Orach Chayyim 299:10)  teaches that every Saturday night Miriam's well moves through all the waters of the world, bringing healing to those who are ill and suffering.  In modern times, some place a cup of fresh water on the seder table in honor of Miriam.    (pg. 226  The Jewish Book of Days)

• As Mashiach Yeshua stood before the Samaritan woman at the well, he spoke to her of a well, a makor: himself:

"Whoever drinks this water will get thirsty again;
      But anyone who drinks the water that I shall give
      Will never be thirsty again:
      The water that I shall give
      Will turn into a spring inside welling up to eternal life."

    (Yochanan 4:14)