Is there a name for these "pouring" clouds?
The term used by the American Meteorological Society is orographic fog. A perhaps more descriptive name is "orographic waterfall cloud".

Prevailing winds can force air to flow upwards over rising terrain. The rising air cools more or less adiabatically, and this can in turn result in clouds. The nature of the orographic clouds (orographic: "related to mountains") that result vary greatly.

In arid regions, orographic clouds can form lenticular clouds that look amazingly like UFOs (three links). Unstable conditions can result in wave clouds, where an obstruction causes a cloud after cloud after cloud downwind of the obstruction. Even icebergs can cause wave clouds. Another form of orographic cloud is a banner cloud, where a cloud flies like a banner downwind of a mountain:


Source: https://commons.wikimedia.org/wiki/File:Banner_clouds.jpg . Copyright Zacharie Grossen, license CC BY-SA 3.0

This is getting closer to an orographic fog. Climbers on the Matterhorn oftentimes experience that cloud, firsthand. Even closer to home is Table Mountain near Cape Town, South Africa.


Source: https://commons.wikimedia.org/wiki/File:Cape_Town,_Table_Mountain,_Table_Cloth.jpg. Copyright KodachromeFan, license CC BY-SA 3.0

This is an orographic fog. (Table Mountain can also create some rather spectacular lenticular clouds.) Another example of an orographic fog is detailed in the article "Waterfall-like Orographic Clouds".

The conditions needed to form an orographic fog include


Prevailing winds that force air to blow upwards over an obstruction, with the orographic fog flowing downwind from the obstruction.
The flowing air must be sufficiently humid. Without this condition, you might see a very cool looking lenticular cloud, but you won't see a banner cloud or an orographic fog.
The flowing air must be sufficiently cool. Humid air at the same pressure and temperature of arid air is less dense than is that arid air. The flowing humid air has to be fairly cool for the flow to be downward downwind of the obstruction.
The flow has to be fairly slow (low Reynolds number) and uniform (low Froude number). Otherwise, a wave cloud or banner cloud will result.