The story that the 372nd MP company is returning to Iraq is interesting and stresses the relevance of the question of identity over time: what constitutes the same unit? As you may know, this is the unit whose members committed the events that we now know as the Abu Ghraib torture scandal. But is the same unit really returning to Iraq? Should we worry that because it is the same unit they might do the same thing? The unit, whatever that is, was never punished though some if its members were and some of it superior officers were.
Clearly it is not the fact that the unit retains the same people that keeps the unit the same over time. Units have people come and go all the time. We don't even know how many soldiers who were members of the unit during the scandal are still in the unit. (Units lose lots of members after deployments and I am sure the 372nd lost more than most.) Geographically, units move, so their identity is not tied to a physical place. Unit's missions change as well, so that too cannot be the source of "the same unit". . . It is very much a Ship of Theseus issue. In this case it seems like a real-world question where our theory of identity is relevant to how concerned we need to be about the future of this unit. Moreover, the unit will undoubtedly get close scrutiny because people believe that it is the same unit.
On a practical level, because of the scandal this unit has undoubtedly received very serious training and warnings so that they will not repeat the mistakes the unit made in the past, but what should we expect of the unit?
Clearly though there is something that keeps this unit the same as it was the first time it was deployed. Its designation is the same. The unit's reputation is damaged, perhaps irreparably. It is a worthwhile question for philosophers of military things.