If you want your unit to be able to move, you have to keep the move, patrol, defend, and stop icons.
If you want your unit to be able to attack, you have to keep that icon too.
There is a way to rearrange them if you are interested in doing that.
Make the unit a ward, it removes most of those buttons.
It removes all buttons on the unit's UI. The only order a player can give the unit is "smart" (right-click). Ward units can still move/attack/stop/patrol/hold position/cast abilities/etc., but players can't directly order them to do so. You'll need to give those units the orders via scripts/triggers.
for real? why would you want to do that? the only reason I can see for getting rid of the standard command UI is to make room for more ability icons...
It also wouldn't "make room" for icons. No icons will be visible for the unit.