There is one single point in the Earth's orbit where it is closest to the sun. That point is called the "perihelion".
I don't think such a point has a special name. Perhaps you are thinking of the Lagrange points, but that's not exactly the same.
The Tropic of Cancer.
A comet's tail points away from the Sun. This happens because the solar wind pushes the comet's gas and dust particles away from the Sun, forming a tail that always points in the opposite direction of the Sun.
That happens at the time when the sun passes the "solstices", which are points on the map of the stars. Those days themselves are often called the solstices, but that's incorrect.
It's called the beginning of Winter in the northern hemisphere, and it's called the beginning of Summer in the southern hemisphere. On that occasion, the sun passes one of the two points called "solstices" on the map of the stars.
The points where the sun reaches the greatest distance north or south of the equator are called The Tropics of Cancer and Capricorn. At one time the sun was in those constellations when it reached those points. It has shifted due to precession of the poles. It will be back in them in about 20,000 years.
A Comets tail points away from the sun.
The high points in an elliptical orbit are called apogee, while the low points are called perigee. Apogee is the point farthest from the center of the body being orbited, while perigee is the point closest to the center.
sun spots
Away from the Sun.
In North America, the season when the north pole points toward the sun is Summer.