We use the cloud naming system invented in 1802 by Englishman Luke Howard. To describe clouds he used Latin names: the first part of the name describes height, and the second part describes shape.
Prefixes for height
cirro = high clouds - above 6 km
alto = midlevel clouds - between 2 and 6 km
no prefix = low level clouds
Names for shapes
cirrus = curly or fibrous
stratus = layered
cumulus = lumpy or piled
To indicate that a cloud can produce precipitation, you should add nimbus.