How does the way someone talks contribute to their identity?
This is an interesting question. Let me give you a few points.
First, people make judgments about one another by external things. So for example, the way a person dresses says something about that person. In the same way, a person's speech reflects that person in some way. This contributes to a person's public identity.
Second, the way a person speaks is also usually tied to social and economic class. The proper use of English is a marker of education and privilege, at least to some degree. So, this, too creates identity as well.
Third, we can also say that a person's speech can also gives off regional influences as well. So for instance, a person from Boston speaks in a certain way, which is different than someone from Atlanta.