What is the Moon's extremely thin atmosphere called?

The Moon’s extremely thin atmosphere is called an exosphere.

A lunar exosphere is so sparse that the Moon is effectively surrounded by vacuum for most practical purposes. Unlike Earth’s atmosphere, it is not a dense, layered blanket of gas that supports weather, clouds or human breathing. Individual atoms and molecules are spread extremely thinly around the lunar surface.

The exosphere is continually replenished by several processes. Solar-wind particles and ultraviolet light can knock atoms from the surface, a process called sputtering. Micrometeorite impacts and radioactive decay inside the Moon can also release gases. Because lunar gravity is weak and the surface is exposed to space, many particles eventually escape or are swept away.

The exosphere contains unusual traces of gases and elements, including helium, neon, argon, sodium and potassium. “Atmosphere” is scientifically acceptable as a broad description, but exosphere is the specific name. Magnetosphere, stratosphere and troposphere are not correct: the Moon does not possess Earth-like atmospheric layers, and it lacks a global planetary magnetic field.