I always tie in-between the ends. This way the line is only going around one wire instead of two. I do this so the knot is tight on the split-ring. When I tie it around both wires, the knot has a tendency to stay loose and cause problems by sliding around the ring and catching on the ends. By tying in-between the ends, the knot stays tight on the ring and hardly moves. When it does move, it just butts up against the ends of the ring. I’ve never noticed it damaging the line or knot by doing this.
Depending on the lure, I remove the split-rings to begin with anyways.