I relate to identity issues, it's a key trait of having BPD...Much of the time I don't know 'who' I am.
Let's look at identity for a second:
"Identity may be defined as the distinctive characteristic belonging to any given individual...The term comes from the French word identité, which finds its linguistic roots in the Latin noun identitas, -tatis, itself a derivation of the Latin adjective idem meaning "the same." Weinreich gives the definition "A person's identity is defined as the totality of one's self-construal, in which how one construes oneself in the present expresses the continuity between how one construes oneself as one was in the past and how one construes oneself as one aspires to be in the future.''

Okay, so I've found that with my BPD, it's not that I don't have an identity, it's that my PERCEPTION of my identity is lacking. So if identity is defined as characteristics that remain sound and consistent across the board and in all situations, we can maybe find some relief in writing down what we know to be true and consistent about ourselves.

For instance, although my physical characteristics may change (ie. I may dress and look different at work vs. home) and some of my demeanor changes (ie. I may talk a certain way at work and exude confidence as opposed to a more casual attitude at home) parts of me don't change. I know there are parts of me (as there are parts of everyone) that can't be modelled after another person or an idealization. My values, for example. I know in my heart what I feel to be true and important, this remains consistent always (ie. if I know kindness to be good above all else, that value doesn't sway depending on who I'm with). Also, my interests: I know I like to play guitar, make art, read...this is part of my identity. Other parts of my identity: my gender, my orientation, my ethnicity, my culture, my religious or political beliefs...general characteristics. Although we may be the confident mediator around coworkers, the skateboarding relaxed girl around friends, and the sarcastic comedian around family, I think we all do these levels of 'shifting' whether we have mental illness or not.

So what do you know to be true about yourself? Something that is defined by only you?

At least looking at these things helps me to realize it is mere perception rather than fact. My identity is there, it's the view of myself that changes.