I know of at least big title game (Starcraft II) that doesn't require unique display names, so it would seem like it can work in at least some circumstance.

Under what situations does allowing non-unique display names work well? When does it not work well?

Does it come down to whether or not impersonation of someone else is a problem?

The reasons I believe it works for Starcraft II is that there isn't any kind of in-game trading of virtual goods and other than "for kicks" there isn't much incentive to impersonate someone else in the game. There's also ladder rankings so even trying to impersonate a pro is easily detectable unless you're on a similar skill level.

What are some other cases where it makes sense to specifically allow or disallow duplicate display names?

(I have no idea what to tag this as. I went with game-design because I needed at least 1 tag and I don't have rep to create new ones yet.)