Stone veneer fireplace with TV mount and mantle
If you use actual cement board, actual mortar, and actual stone, it will hold together due to a chemical reaction that basically turns the stone, mortar, and rock into a single piece of rock.  Just make sure NOT to use too much water in the mortar.  It should be almost like playdough.  The biggest mistake people make with mortar (and other cement) is making it thin like vomit.  Make sure to wipe the cement board with a wet sponge before placing the rock on it.
Once everything is together and hardened you can drill into the rock facing and use concrete anchors if you want.  That is what I would do in case I ever wanted to remove the TV mount and replace it with a different one.
This job can be easier if you buy stone that has been rock-sawn in half (so that the &quot;back side&quot; going against the cement board is smooth)