This is a strange question for me because this is so extremely common, but I have never heard a name to describe exactly what it is.
This is commonly used to provide water to animals from a trough or tube at a constant water level without dripping. As the water in the trough is reduced in height from drinking, air bubbles enter the reservoir which then releases sufficient water from the container to refill the trough and stop further air from entering the container.
The remaining liquid is held inside the container by the vacuum above the water, and atmospheric pressure holding the water up in the evacuated space, even though the bottom remains open.
And this reservoir container is formally called a.... ?