My motor came with a black ring attached to the bottom of the rotor. It spins along with the rotor, and it's not exactly a ring shape since it's open at one end - kind of like an omega symbol or like a stag beetle's horns. What is it called and what is it for?
That is a circlip (or C-clip) - it looks like it is used here to prevent the shaft from coming out of the bearing.
From the Wikipedia link above:
A circlip (a portmanteau of "circle" and "clip"), also known as a C-clip, Seeger ring, snap ring or Jesus clip, is a type of fastener or retaining ring consisting of a semi-flexible metal ring with open ends which can be snapped into place, into a machined groove on a dowel pin or other part to permit rotation but to prevent lateral movement. There are two basic types: internal and external, referring to whether they are fitted into a bore or over a shaft. Circlips are often used to secure pinned connections.