This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
The Mysterious Benedict Society
Milligan continues to go by "Milligan" even after he get his memories back because when it comes to his former identity, he feels That Man Is Dead.
Even after Milligan gets his memories back at the end of the first The Mysterious Benedict Society book, he still continues to go by "Milligan" and his real name is never revealed. Perhaps the events that happened to him changed him so much that he doesn't feel comfortable using his original name anymore.