Identity formation and development among various groups and (sub)cultures has been very well-researched. It's not the specific group, but the general principles and theories that you can apply to your research interest. Search around Googlescholar, good luck!
Yes, there is an immense amount of literature around identity, identity politics and identity in relation to other concepts like heritage, memory, etc. But I do not really understand your question. First you write "their identity" and then "various identities". Do you presuppose a common collective identity or not?
The question of identity and its constant restructuring is a key issue and concept of sociology, my area of expertise. I think the approach of Iranian Azerbaijanis and the formation of their identity should not ignore the contribution of Giddens through his work - Modernity and personal identity. Central work of the approach of identities in the present times. The symbolic interactionism puts the priority on interaction processes, the action has as its aim the achievement of pre-defined objectives, as also it results from the interaction between two subjects. According to Goffman, the interaction between people is conceived as theatrical representation (1993). The self is constructed also for control of the impressions we cause. The same author distinguishes between two types of social identities: the virtual social identity, which is built from the sum of the information about the "self" gathered in the interaction - physical aspects, reputation, ways of talking, ways of dressing, etc., and real social identity, made up of the own attributes, ie real ones, of the people. Some of these attributes involves the immediate "discredited" of individuals who own them. If the attributes that give discredit fail to report immediately in the course of social interaction, the individual tends to hide them, through tactics by matching his virtual social identity to his actual social identity. From this perspective, identity construction processes feed on the references provided by the representation. The analogy with the linguistic communication is illuminating: Goffman defined "frontstage", as "the expressive and standardized equipment intentional or unconsciously employed by the individual during his representation", calling attention to the fact that certain frontages become a "collective representation".
As we have seen, in the sociological discussion of identities, it's important to reveal the inseparability of identity, self and society. Thus, an analysis component of these issues lies in understanding the social context in which the self and its constituent parts (identities) act, "the nature of the self and what individuals do depend, to a large degree, on the society in which they live" (Stets & Burke, 2003:1).
FEATHERSTONE, Mike (1995) – Undoing culture: globalization, postmodernism and identity. Londres: SAGE Publications. ISBN 0-8039-7606-2.
HALL, Stuart; DU GAY, Paul, eds. (1996) - Questions of cultural identity. Londres/Thousand Oakes/Nova Deli: Sage Publications. ISBN 0 8039 7882 0.
LEARY, M. R.; TANGNEY, J. P., eds. (2003) - Handbook of self and identity. Nova Iorque: Guilford Press. ISBN 9781593852375.
HERMANS, Hubert (2002) – The dialogical self: one person, different stories. In KASIMA, Yoshihisa, FODDY, Margaret; PLATOW, Michael (eds.) - Self and identity: personal, social, and symbolic. Nova Jersey: Routledge. ISBN 9780805836837. 71 - 99.