First thing is that it is not the shadow of anything. The side where sun's light is absent.
We call it as new moon as a new phase has begun to reach the stage of full moon.
Even that might have been named as NO MOON, and misheard as NEW MOON.
The shadow of the Earth on the moon's surface is the reason that it takes different phases. When the Earth completely occludes the moon, it is a new moon, and when there is no shadow, it is a full moon.
New moon (the Earth goes into the shadow of the Moon) Lunar eclipses occur at full moon (the Moon goes into the Earth's shadow)
New Moon
The new moon is visible once a month when the moon is blocked by the Earth's shadow
It is a lunar eclipse.
Solar Ecllipse.
A solar eclipse occurs when the Moon's shadow falls on the Earth, blocking the Sun's light.
When the moon is within the shadow of the Earth, a lunar eclipse occurs. When the shadow of the moon falls on the Earth's surface, a solar eclipse occurs.
This is an eclipse of the moon.
The dark shadow caused by the moon on Earth is called the umbra during a solar eclipse.
"Umbra" means "shadow". When the Moon enters the Earth's shadow, we call that a "total lunar eclipse".
Becausec the Moon is nearer the Sun than the Earth at New Moon.