Stamping them, either with individual letter and number stamps or with a one piece stamp that holds the complete mark, can upset the case head & primer pocket quite a bit.
You are displacing metal and it has to go somewhere.
It takes a lot of force to imprint with a single unit stamp having all that lettering on it.
During mfg, the case is held in a die to control deformation and additional processes are done after the marking to insure dimensions are correct.
A pantograph , either a drag or rotary cut might work OK.
As Mike says most of the equipment is computerized now, even the trophys shop stuff.
If there are existing headstamp(s) on the brass it will show under the new marking.
