Why was the movie 'The Ring' called that?

Because it's the last image on the tape, and the last image the victims see before they die. That's the tagline for the movie: "Before you die, you see the ring."

The ring is the last image on the tape and the last thing the victims see before they die because it is the last thing Sadako/Samara saw before she died: the ring of light coming through the lid of the well.