What is the proper term for etching or digging of wall to hide conduit of cables

Solution 1:

It's called chasing. It took three goes to find this use in a dictionary to support this assertion.

1. a : to ornament (metal) by indenting with a hammer and tools without a cutting edge

   b : to make by such indentation

   c : to set with gems

2. a : groove, indent [q.v.]

   b : to cut (a thread) with a chaser

— Merriam-Webster

Etymology from French enchâsser - to set (precious stone). It appears unconnected with chase meaning "to hunt etc", which is from the old French chacier later chascier by 11th century chaser. (OED) However a Northern French variant is written cacher, which is of course modern French for "to hide". One suspects there may be a connected root here. As we have noted before we are not authoritative on French etymologies.

Solution 2:

In the UK it is called chasing:

When running cables or pipes up (or along) a masonry wall, the neatest method is to bury (or, in builders terms, chase) them in the wall surface.

(From a DIY site)

Although this meaning doesn't appear in dictionaries I have checked, it probably derives from:

chase2: Engrave (metal, or a design on metal)

Edit: Just noticed that Merriam-Webster has this definition, which is closer:

2a : GROOVE, INDENT

b : to cut (a thread) with a chaser

Oxford Dictionary

I have also heard "channelled" used in this context.