Best thing i can say is just be there. no advice, no attempts, no suggestions. For myself, i would push those away.
When she wants to talk, be there... encourage her. If that opens up, you can mention that you have some resources if she would like them and then let it go at that.
you could even say you've done some research on DID so you can understand more of what she is going through. It is hard to find words for... somethings are so subtle.

Depression could be a part of it, sure, as could anxiety and a host of other things. Each alter can have their own dx.
good luck!