Most engraving is done with a diamond or carbide cutter, can be done on a mill with a 5th axis or a plate engraver.
I was going to get a used one, but even then the cost was
high enough that it is cheaper to have it done. All my actions are engraved with a CNC milling machine. The biggest part of having a bbl engraved by like a trophy shop is them not being able to hold the bbl in their machines. You need a special vise or holding set up. Electric engravers do the best work, simple scratch type leaves a faint outline. Find someone who cuts name plates, the plastic ones and see if they can hold your barrels, then they need a carbide cutting tip, the results are very nice.
Dave