That line is called diameter. It divides a circle into two semi circles.
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No, a secant line does not pass through the center of a circle. A secant line is a line that intersects a circle in two distinct points. Only a line passing through the center of a circle is called a diameter.
A line that goes through a circle is a secant line. (Remember that a line is infinitely long.) Anyline that passes through a circle is a secant line, whether it passes through the center of the circle or not. Compare this to a line segment with endpoints on the circumference of a circle. That segment is called a cord of that circle. If the cord of a circle passes through the center of that circle, it is a diameter of that circle, which is the longest cord of the circle.
This is called the diameter of the line that passes through the center of the circle. Half of that line is called the radius.
This is a line segment called a diameter of the circle.
A line through a circle that does not go through the center of the circle is a secant line. A line through a circle that does go through the center is still a secant line, by the way. Compare this to a line segment that has its two endpoints on the circumference of the circle. That line segment is a cord of the circle. If that cord of the circle passes through the center of the circle, then the cord is a diameter of that circle.