The Brotherhood of Steel holotag is carried by every member of the order. When a member of the order falls in battle their tags are handed over to the Brotherhood of Steel scribes so their deeds can be recorded in the scrolls. In the Commonwealth they cannot be handed over to the scribes.
↑Elizabeth Jameson: "Which is why I must now ask you for your help. Each Brother wears a Holotag like the one you found. Should you find any of the fallen Brethren in the field, I ask that you return their tags to me, so that I might record their deeds in the scrolls." (Elizabeth Jameson's dialogue)