In oceanography, they are usually called "trenches".
a deep, steep-sided, narrow river valley
A deep valley with steep sides would be called a gorge or canyon.
A ravine.
A ravine is a narrow, deep valley with steep sides typically formed by water erosion. It is often characterized by its rugged terrain and lack of vegetation.
A canyon is a deep narrow valley.
Canyon
Such structure could be called a Canyon.
the river running through rock wear it down into deep valley with the steep sides what is it called
Canyon
Canyon
There are more than one term for a deep narrow valley. Glens, canyons, ravines, fjords are terms you could use.
subduction