Some do, but most don't. A few moons in the solar system have very tenuous atmospheres. Titan, Saturn's largest moon, is the only one in our solar system to have a substantial atmosphere.
Mercury has no moons and no atmosphere. Venus has an atmosphere but no moons. Mercury probably has no moons and no atmosphere because it is very close to the sun.
Mars' moons have no atmosphere
The moon does not have an atmosphere.
There is no atmosphere on the moon. There is insufficient gravity to keep an atmosphere there.
Zero
Titan
The moon has no atmosphere. No air!
The planet Mars is the only planet known with two moons and a predominantly CO2 atmosphere.
No. The moons of Mars are far too small to have atmospheres.
it is considered as an exosphere
PLUH
Our moon has no atmosphere to touch.