I don't know how one would define an 'identity'... self knowledge, I guess? I know who I am. I am me! I know what I like, what I don't like, I make choices about what I will and won't do, I know what I did yesterday, and last year, and what I plan to do tomorrow, etc, etc.

There are other 'self identifying states' within me that are not me. For instance, one whom I shall call P. She is not me. I am not her. Her experience is hers, and my experience is mine. There is no confusion between us about what is her and what is me. When she is out she is herself. Nowadays I am most often aware of when she is out, but I still experience myself as me and know that she is not me. Previously when she was out I had no awareness whatsoever. It was 'missing time' for me.
Now there is a group of us that blend somewhat. We used to be very distinct and individual, but now we tend to operate as one, most of the time. Even when we are blended I can still identify traits or behaviors that formerly belonged wholly to one identity or another.

I think a feeling of emptiness and lack of a stable identity - or different / changing experiences of 'self' - is more often related to BPD than DID. My understanding is that it is more like one identity that changes and presents in different ways... sometimes outgoing and fun, other times withdrawn and depressed etc. The mood states are quite discrete and separate but there is one 'I' that experiences them all, even though there is quite a lot of dissociation going on.