but whenever people were arguing for that theory, we got a lot of replies that it made no sense for the DO to kill Lanfear unless there was no way to retrieve her alive and thus she died in Sindhol because Moridin had to kill her or the Finns did, and it had nothing to do with any idea of punishment.

Mind you, this in part had to do with the fact I was arguing that I was sure killing Lanfear was part of her punishment, and I wasn't so sure though it had happened in Finnland (I was arguing it was also possible it had been done at SG after her rescue, to punish her).

The confirmation by Moghedien that the killing of Lanfear was meant to punish her, thus that there was other ways to retrieve her but Moridin/the DO chose that one to punish her, means my reasoning wasn't crazy at all after all: stripping Lanfear of everything that made her Lanfear was absolutely intentional. She's the only transmigrated Forsaken whose former identity is completely taboo. It's part of her punishment that Lanfear is 100% gone. The others must use their new names and all, but they make no secret of who they were, and of the fact everyone knows. For Cyndane, it's "don't ask, don't tell". Cyndane herself has likely been warned she'll be punished for giving the others any signs of who she were.