What is the name of two points of intersection?
You can give them any name that you like. Conventionally, points are named by capital Roman letters but you do not have to stick by that. You could, if you wanted to, name them after your best friends!
The intersection of two or more mathematical objects is the set of all points that are common to all of them. In set theory, that would be the elements in common. In geometry, it would be the set of all points in common. For example, the intersection of two different planes is a line; the intersection of a plane and a cone are the conic sections: circle, ellipse, parabola and hyperbola.
The properties associated with the angles of a circle is the amount of rotation about the point of intersection of two lines in order to make one line into correspondence with the other. The arc of a circle consists of two points on the circle and all of the points on the circle lie between those two points.