You’re not going to like this answer, but don’t. While it can be okay to write about a character with DID if they simply happen to be in your story, their having DID should not be the focus of the story. That is not your story to tell.
To put this into perspective, let’s imagine a white writer decides they want to write about the experience of what it’s like to be black in America. They want to do that as ethically as possible and ask lots of questions to ensure they’re doing it right. Is that okay? No. As a white person, they should not be writing about someone else’s experience like that. They’ll never fully understand what it means to be black in America.
That said, would it be wrong for them to write a black character into their story? Of course not. Could there be moments where issues of race come up where they consult people to ensure they’re handling it ethically? Yes. But the entire point of the book shouldn’t be to tell someone else’s story.
If we replace that example with DID, this makes more sense, right? DID is fascinating to many people, and they want to write about it. Their hearts are in the right place – they see the media misrepresent us and want to do it right. However, it’s not their story to tell. Plenty of systems are capable of writing and creating their own art. Boost our voices and support our projects, but don’t try to be our voice. Sure, you can write a character who happens to have DID, but please DO NOT write about someone’s lived experience with DID. Unless you have the disorder, you’ll never fully understand. Recognizing that is the sign of a true ally.