Some definitions of identity

Rebecca Black
Black argues that "identity" is "the ability to be recognized as a 'kind of person' … within a given context" (Black 2007: 118).

Angela Thomas
Being recognized as a certain 'kind of person', in a given context, is what I will mean by 'identity'.  In this sense of the term, all people have multiple identities connected not to their 'internal states', but to their performances in society." (Thomas 2007: 166).

Jon Marshall (2007)
"Identity is a process of categorization which involves the allocation of membership of people into groups.  I am an academic, a footballer, a soldier, a wife, etc.  The properties of the group are emphasized in relation to other groups and to the situation (p. 27). … People categorize themselves and are categorized in relationship to other groups.  These categorizations are related and dynamic, as people attempt to determine the attributes which allocate themselves and others to various groupings and demonstrate closeness to group prototypes.  People may have differing self-categorizations as members of different groups, some of which will change during their lifetime, and others of which (as appear with gender), are always relevant.  Identity categories are not just chosen but imposed." (p. 23)

James Paul Gee
Discourse can be seen as the underlying principle of meaning and meaningfulness. We "do life" as individuals and as members of social and cultural groups—always as what Gee calls "situated selves"—in and through Discourses, which can be understood as meaningful co-ordinations of human and non-human elements. Besides people themselves, the human elements of co-ordinations include people's ways of thinking, acting, feeling, moving, dressing, speaking, gesturing, believing, and valuing. Non-human elements of co-ordinations include such things as tools, objects, institutions, networks, places, vehicles, machines, physical spaces, buildings. And "[w]ithin such co-ordinations we humans become recognizable to ourselves and to others and recognize ourselves, other people, and things as meaningful in distinctive ways" (Gee, 1997, p. xiv).

References

Rebecca Black (2007). Digital Design: English language learners and reader reviews in online fiction. In M. Knobel, & C. Lankshear. (Eds.), A new literacies sampler (115-136). PeterLang: New York.

Gee, J. (1997). Foreword: A discourse approach to language and literacy. In C. Lankshear, Changing Literacies. Buckingham: Open University Press.

Gee, J. (2001). Identity as an Analytic Lens for Research in Education. Review of Research in Education, 25, 99-126. Washington, DC. W. G. Secada, American Educational Research Association.

Marshall, J. P. (2007). Living on cybermind: categories, communication, and control. Peter Lang Publishing: New York.

Thomas, Angela. Blurring and breaking through the boundaries of narrative, literacy, and identity in adolescent fan fiction. In M. Knobel, & C. Lankshear. (Eds.), A new literacies sampler (pp. 137-165). Peter Lang: New York.