Good question. !!!!
The barrel ID is very Important and at the minimum should have the exact cartridge name on it.
From there, it should identify any changes to the SAMMI cartridge, like AI, Neck diameter, throat length if shorter than standard, shoulder angle if different than standard 40o for an AI.
Lead angle and other changes that don't contribute to excessive pressure, are nor required.
Next comes the voluntary engraving such as Gunsmith, and commemorative engraving. (Quotes, sayings, honoring someone, Even the rifles name if you have a streak of redneck in you
. These markings are normally on the other side of the required barrel markings.
Some don't bother marking the barrel because it belongs to them and they know what it is. the problem when they pass on, the recipient of the weapon, may not have a clue what it is. I have seen many cases of this, and for safety they had to go to a smith and find out what it was. Even then, it is hard for a smith to measure a chamber for every subtle change that can be made and a chamber case is the closest way.
So as a minimum you should place the cartridge name and any pertinent information in the barrel Id.
J E CUSTOM