I'm just wondering about the assumption itself -- if Lupin's prior affiliation with Dumbledore, his role in Harry's parents' past and his actions during Prisoner of Azkaban as well as Order of the Phoenix still enabled him to go undercover for the duration of HBP... why is everyone assuming that his participation in the fight with the Death Eaters would blow his cover? The fight itself sounds like it was happening mostly in darkness with a lot of confusion -- a Death Eater was even killed by another Death Eater's Killing Curse, for example. I'm thinking Lupin's "deep cover" goes quite a bit deeper than changing his name, is all, because there is plenty of readily available canon evidence for any Death Eater worth his salt knowing about Lupin's true affiliation and knowing what he looks like.
It might be Snape, obviously -- but Snape's ESE status is still questionable. If Snape is really working for Voldemort and has been all this time, sure, he'll blow Lupin's cover. But if he hasn't been? Hmm.
The words "concealment" and "disguise" come to mind. XD