I am mostly sure the answer is yes, but I'd like to know if this would bother or confuse you as a reader.
My character (we'll call him Jack) goes through an identity crisis throughout the story and at different points (believing he is one person or another) other characters refer to him by this new name, which he also accepts hismelf to be, but I always tag him as Jack.
Example:
Jack discovers he is Joe.
And in the face of compelling evidence Jack realized he was Joe. "How are you today Joe?" Someone said from behind him.
"I'm great," Jack replied."
The reason for thsi si his "identity" alternates and so I want a universal one to keep things consistent. The alternative is to change his name each time but I think that will be even more confusing.
If you are Full Omni, I think the POV/ narrator could call him "Jack" even though other people refer to him as "Jill."
If it's his POV, he needs to consitently use however he thinks of himself. If that changes over time, his internal tag can change too.
If it's 3rd person and not this character, refer to Jack however that POV does even if no one else is.
I think your bigger problem is making sure that the reader can keep up with the name changes.
I have an MC in my WIP that is referred to by a number of names at various times because she is in hiding. It's Full Omni so the non-dialog tags are always the same name even if everyone else in the scene is calling her something else. As long as it is in POV and clear, you should be okay. At least that's my 2 cents.
If it were me, I would go with referring to him by the name he thinks of himself by. But that's me.
[This message has been edited by JeanneT (edited July 23, 2007).]
I wouldn't recommend it as a way to write, though.
I agree that a character must only refer to himself as how he identifies himself. But I forgot to mention that our character sees himself as Jack form the beginning and later learns he is also John, and later learns he is, instead of John, Larry. But He also sees himself as Jack from start to finish. Larry and John are mutually exclusive people, but Jack is akin to him no matter whether he was Larry or John, kind of like a nickname or a codename, along those lines.
I remember a Heinlein story, "Gulf," who starts with one name and identity beginning with "A" to get through security first, switches name / identity immediately after and stays that for awhile, resurfaces at a later point apparently as himself (or at least another name), sticks with that awhile, and then becomes someone else at the end before his violent death. Justifiable, but I don't think I "got" the story until I reread it more recently---and not that I think as well of it as I do of other Heinlein.