I have had some accommodations (am getting some right now in fact) that are related to my DID, without my DID actually being disclosed. Yesterday I talked with one of my study trainers about the stress I have been under at work this year and how greatly it has affected me. I mentioned depression and panic attacks without going into the DID, PTSD and related stuff that is actually at the base of the situation. I am getting some accommodations as a result of that discussion.
So there are ways around it. Many people with DID have other diagnoses as well (eg: depression and anxiety) so it may be easier to discuss these instead of the DID itself.